STACK 

ANNEX 


F.H.5HEPARD 


NEW  YORK 


C .  PODPIC 


TWENTY-FIRST  EDITION— R  EVISED  AND  AUGMENTED 

HARMONY  SIMPLIFIED 

A  SIMPLE  AND  SYSTEMATIC  EXPOSITION 

OF  THE 

PRINCIPLES  OF  HARMONY 


DESIGNED  NOT  ONLY  TO  CULTIVATE 

A  THOROUGH  KNOWLEDGE  OF  CHORD- 
CONSTRUCTION 

BUT  ALSO 

TO  PRACTICALLY  APPLY  THAT  KNOWLEDGE 

AND  TO  DEVELOP 

THE  PERCEPTIVE  FACULTIES 
BY 

F.  H.  SHEPARD 

AUTHOR  OF  "HOW  TO  MODULATE,"  "A  KEY  TO  'HARMONY 

SIMPLIFIED,1"  "CHILDREN'S  HARMONY,"  "GRADED 

LESSONS  IN  HARMONY,"  ETC. 

Price,  $1.50,  net 

NEW  YORK 

G.  SCHIRMER,  INC. 
3  E.  43d  STREET 


Copyright,  1896,  by  G.  SCHIRMER,  INC. 


Printed  in  the  U.  S.  A. 


PREFACE. 


This  little  work  offers  no  apology  for  its  publication. 
It  aims  at  the  following  distinct  objects: — I.  To  treat 
tL*  subjects  of  Scales,  Keys,  Signatures,  and  Intervals  so 
thoroughly  that  the  pupil  will  be  prepared  to  understand 
with  ease  the  principles  of  chord-construction. — II.  To 
present  the  subject  of  Chord-Construction  in  such  a  man- 
ner that  the  pupil  will  be  obliged  to  form  all  chords  him- 
self, thus  deriving  a  practical  knowledge  of  the  subject. — 
III.  To  discard  all  arbitrary  rules.  Instead  of  blindly 
struggling  with  a  mass  of  contradictory  rules,  the  pupil 
is  made  acquainted  with  the  original  principles  from 
which  the  rules  are  derived,  and  his  judgment  cultivated 
to  apply  them  with  discretion. — IV.  The  principles  of 
the  natural  resolution  of  dissonances  are  shown,  instead  of 
giving  the  rules  for  the  resolution  of  chords  of  the  seventh. 
The  pupil  will  apply  these  principles  not  only  to  chords 
of  the  seventh,  but  to  all  fundamental  dissonances.  — 
V.  The  chords  of  the  Dominant  Seventh,  the  Diminished 
Seventh,  the  Major  and  Minor  Ninth,  and  the  Italian, 
French  and  German  Sixth,  are  shown  to  be  but  diffeient 
forms  of  the  same  chord,  with  a  perfectly  uniform  reso- 
lution, thus  enormously  i  educing  the  difhcuicy  o£  under- 
standing these  harmonies,  and  diminishing  the  complex- 
ity of  the  whole  Harmonic  System. — VI.  The  system  of 
"  Attendant  "  Chords  will  be  found  very  helpful  in  under- 
standing those  chords  which,  though  outside  the  key, 
evidently  are  closely  related  to  some  of  its  triads.  It  is 
also  of  much  assistance  in  reducing  the  art  of  Modulation 


2223840 


iv  PREFACE. 

to  a  condition  in  which  it  can  be  studied  step  by  step. — 
VII.  After  the  regular  course  in  chord-connection  is  com- 
pleted, a  supplementary  course  of  study  is  outlined,  in 
order  to  gain  proficiency  in  practically  using  all  the  means 
of  giving  variety  to  a  composition  or  improvisation.  This 
proficiency  is  indispensable  to  young  composers  and 
organists,  but  it  is  usually  allowed  to  develop  itself,  as 
nearly  all  manuals  of  Harmony  stop  at  this  point.  To 
expect  a  pupil  to  be  able  to  introduce  Suspensions,  Pass- 
ing-notes, Sequences,  Anticipations,  etc.,  into  his  improv- 
isations, or  even  into  his  compositions,  after  reading  the 
explanation  of  them,  is  like  explaining  to  a  novice  how  the 
Piano  is  played,  and  then  expecting  him  to  be  able  to  per- 
form.— VIII.  A  course  in  the  Development  of  the  Percep- 
tive Faculties  is  given,  training  the  pupil  to  listen  intelli- 
gently to  music,  to  distinguish  between  the  various  chords, 
etc.,  and  to  write,  in  musical  notation,  what  he  hears. — 
IX.  A  chapter  on  Musical  Form  is  added,  together  with 
suggestions  in  regard  to  the  Analysis  of  standard  works. 

Owing  to  the  pressure  of  professional  duties,  as  well 
as  to  the  consciousness  of  his  inability  to  improve  on  them, 
the  author  has  taken  the  exercises  with  figured  basses 
chiefly  from  the  "Manual  of  Harmony"  by  Jadassohn, 
and  the  "Manual  of  Harmony"  by  Richter,  indicating 
the  exercises  of  the  former  by  the  letter  J.,  and  those  of 
the  latter  by  R.  These  exercises  are  supplemented  by 
others,  designed  for  special  purposes. 


TABLE   OF   CONTENTS. 


PART   I. 

SCALES:  KEYS:   INTERVALS. 

SCALES  AND  KEYS. 
CHAPTER  I,  pp.  3-25. 

The  major  scale  —  Sharps  and  flats  —  Double  sharps  and 
flats — Keys  —  Signatures — Circle  of  keys  —  To  distinguish  keys 
having  many  sharps  or  flats  —  Relative  sharpness  of  keys  and 
notes — Related  keys — Specific  names  of  scale-notes — Rela- 
tive minor  —  Chromatic  and  Diatonic  —  Synopsis— Historical  — 
The  perceptive  faculties. 

INTERVALS. 
CHAPTER  II,  pp.  25-42. 

General  names  —  Specific  names  —  Standard  of  measurement- 
Major,  minor,  augmented  and  diminished  —  Extended  and  in- 
verted—  Consonant  and  dissonant  —  Application  of  terms- 
Definitions  —  Enharmonic  —  Historical  —  Perceptive  faculties  — 
Complementary  Intervals. 

PART  II. 

CHORDS. 
TRIADS. 

CHAPTER  III,  pp.  43-66. 

Foundation  of  the  harmonic  system — Natural  harmonics  — 
Triads  —  Marking  —  Specific  names  —  Principal  and  secondary  — 
Doubling  —  Position  —  Four-part  writing — Connection  of  triads 
—  Consecutive  fifths  and  octaves  —  Open  and  close  harmony  — 
Connection  of  triads  in  minor  —  Harmonizing  the  scale. 

INVERSION  OF  TRIADS. 

CHAPTER  IV,  pp.  66- 81. 

Figuring — Figured  bass — Hidden  octaves  and  fifths — Per- 
ceptive faculties  — Transposition. 

CHORD  OF  THE  SEVENTH. 
CHAPTER  V,  pp.  81  -  100. 

Its  construction  —  Resolution  —  Inversions  —  On  the  Preparac 


vi  TABLE  OF  CONTENTS. 

tion  of  dissonant  intervals  —  Cadencing  resolution  —  Leading  of 
the  parts — Influences,  combined  and  opposed  —  Directions  for 
part-writing. 

INVERSIONS  OF  THE  CHORD  OF  THE  SEVENTH. 
CHAPTER  VI,  pp.  101  —  105. 

Figuring  and  naming — To  find  the  root —  Resolution. 

SECONDARY  CHORDS  OF  THE  SEVENTH. 
CHAPTER  VII,  pp.  105-127. 

Formation  —  Resolution  —  Preparation  of   dissonant   intervals 

—  Succession  of  chords  of  the  seventh  —  Secondary  sevenths  in 
minor  —  Inversions  —  Cadences  —  Closing  formula  —  Non-ca- 
dencing  resolutions  —  Analytical  and  comparative  review  —  His- 
torical. 

CHORD  OF  THE  DOMINANT  SEVENTH  AND  NINTH. 
CHAPTER  VIII,  pp.  127-130. 

Construction  —  Resolution  —  Inversions. 

CHORD  OF  THE  DIMINISHED  SEVENTH. 
CHAPTER  IX,  pp.  130-136. 

Construction — Use  in  major  —  Similarity  of  sound  —  Resolu 
tion —  Inversions —  Figuring. 

CHORDS  OF  THE  AUGMENTED  SIXTH. 
CHAPTER  X,  pp.    136-145. 

Are  altered  chords  —  Construction  —  Resolution  —  Upon  super 
tonic —  Recapitulation. 

ALTERED  CHORDS:   FUNDAMENTAL  CHORDS. 
CHAPTER  XI,  pp.  146- 163. 

Description  —  Change  of  root  —  To  distinguish  between  altered 
chords  and  foreign  fundamental  chords  —  The  discovery  of  roots 

—  Ambiguous  chords —  Altered  chords  in  general  use  —  Neapo.1- 
itan  sixth. 

FOREIGN  CHORDS. 
CHAFFER  XII,  pp.  163-  170. 

Relation  of  dominant  to  tonic — The  system  of  "attendant1 
chords  —  Their  influence  upon  modern  music  —  Various  forms, 
minor  seventh,  diminished  seventh,  etc. 


TABLE   OF  CONTENTS.  vi 

MODULATION. 

CHAPTER  XIII,  pp.  170-184. 

How  effected — To  connect  any  two  triads — Use  of  "  attendant  " 
chords  —  To  connect  any  two  keys  —  Formula  for  modulation  — 
By  means  of  dominant  seventh  —  By  means  of  closing  formula  — 
By  means  of  diminished  seventh  —  To  any  chord  of  new  key  — 
Change  of  mode. 

PART    III. 

VARIETY  OF  STRUCTURE. 
CHAPTER  XIV,  pp.  185  -  193. 

Suspensions  —  Anticipations  —  Retardations  —  Syncopation. 

UNESSENTIAL  NOTES. 

CHAPTER  XV,  pp.  193-203. 

Passing-notes  —  Auxiliary  notes  —  Organ-point  —  Invertec 
pedal  —  General  recapitulation — Tabular  view  —  Essential  and 
unessential  dissonances. 

MISCELLANEOUS  SUBJECTS. 
CHAPTER  XVI,  pp.  203-213. 

Cross  relation  —  The  tritone  —  Treatment  of  chord  of  six- 
four —  Licenses — Sequences — Related  keys  —  Naming  the  oc- 
taves—  The  great  staff — The  C  clefs  —  Chords  of  the  eleventh 
and  thirteenth — Open  harmony  —  Five-,  six-,  seven-,  and  eight- 
part  harmony. 

HARMONIZING  MELODIES. 
CHAPTER  XVII,  pp.  214  -  223. 

The  cantus  firmus  —  The  chant  —  Speed  in  writing  —  Practi- 
cal application, 

ANALYSIS  AND  FORM. 
CHAPTER  XVIII,  pp.  224-235. 

Method  of  procedure  —  Sonata-form  —  How  to  trace  the 
theme  —  Harmonic  analysis  —  Rondo-Form  —  Primary  form  — 
Phrase  —  Period —  Motive  — Thesis  and  antithesis. 


IMPORTANT. 

NOTE  I.  The  student  is  urged  to  make  frequent 
and  persistent  use  of  the  keyboard  for  all  appropriate 
exercises  here  given,  for  by  this  the  practical  efficiency 
of  the  study  is  greatly  increased.  Exercises  in  Scale, 
Interval,  and  Chord  construction,  in  Chord  connection, 
and  Chord  resolution,  are  suitable,  and  also  the  exercises 
in  Part  Writing,  under  proper  conditions. 

NOTE  II.  For  use  in  Class  Drill  the  "Keyboard 
Diagram,"  published  separately,  is  of  value,  for  by  its 
use  a  large  class  may  receive  the  same  practical  and 
thorough  keyboard  drill  as  the  single  individual  at  the 
piano. 

NOTE  III.  Teachers  (and  those  studying  without  a 
teacher)  are  referred  to  the  author's  Key  to  "  Harmony 
Simplified"  for  nearly  five  hundred  additional  questions 
for  use  in  the  class-room,  and  for  other  hints  in  regard  to 
the  use  of  this  work ;  also  for  solutions  of  all  the  exercises 
contained  herein.  See  p.  24. — "  Graded  Lessons  in  Har- 
mony, by  the  author,  contains  further  material  for  teachers 
and  students. 

.HARMONIZING  MELODIES. 

NOTE  IV.  For  special  work  in  harmonizing  melo- 
dies see  Chap.  XVII.  This  work  may  be  commenced 
after  Chap.  V.,  or  even  earlier,  if  simple  exercises  are 
chosen. 


HARMONY  SIMPLIFIED 


PART  L 


CHAPTER   I. 

SCALES  :    SIGNATURES  :    KEYS  :    CIRCLE    OF    KEYS : 
HISTORICAL  :    THE    PERCEPTIVE    FACULTIES. 

Construction  of  the  Major  Scale. 

1.  A  Major   Scale    is    a    succession    of  eight    tones4 
placed  at  a  distance  of  either  a    Whole  or  a  //iz/^-step 
apart. 

A  Half -step  or  Semitone,  is- the  smallest  interval 
formed  upon  the  Piano-keyboard ;  that  is,  from  any  key 
to  the  next  one,  white  or  black ;  e.  g.,  C  to  Dfr:  E  to  F : 
Afl  to  B,  etc. 

A  Whole  Step  is  a  step  as  large  as  two  Half-steps ; 
e.  g.,  C  to  D :  E  to  FJ :  GJ  to  AjJ :  Bb  to  C. 

2.  The  eight  notes  of  a  scale  are  called  Degrees  of  the 
scale,  and  are  numbered  from  the  lowest,  or  Keynote,  up 
ward  to  the  octave  of  the  keynote. 

3 


4  HARMONY  SIMPLIFIED. 

3.  Notice,  when  playing  the  scale  of  C  on  the  Piano, 
f.hat  from  the  3rd  to  the  4th  "degree,  and  from  the  7th  to 
the  8th,  are  ^a//"-steps,  while  between  all  the  other  degrees 
are  'whole  steps.      This  forms  our  rule  for  the  construc- 
tion of  any  Major  scale,  (  also  called  Diatonic  *  Major 
scale,)  'without  regard  to  the  starting-place.     There- 
fore, we  will  write  the  succession  of  figures,  indicating 
the  position  of  the  half-steps  by  the  sign  - — ',  thus  making 
a  Formula,  or  general  pattern,  by  which  we  can  con- 
struct a  scale  starting  from  any  note  ;  thus  : — 

i      2345678.     Briefly  expressed  for  memo. 

rizing,  this  formula  is  as  follows  : — 

The  ffalf-sivps  are  from  3  to  4  and  from  7  to  8. 
All  other  steps  are  Whole  steps. 

4.  To  illustrate  this  formula,  let  us  begin  on  the  note  G, 
and,  following  the  above  rule,  form  a  scale : — 

G    A    B     C    D    E    F    G.    Let  us  examine  this  step 
i       2     3_4     5      6     7^8. 

by  step,  comparing  the  notes  with  the  formula  : — 

1  to  2  should  be  a  whole  step,  i.  e.,  G  to  A  —  is  right. 

2  to  3  should  be  a  whole  step,  i.  e.,  A  to  B  —  is  right. 

3  to  4  should   be  a  half- step,  i.  e.,  B  to  C  —  is  right. 

4  to  5  should  be  a  whole  step,  i.  e.,  C  to  D  —  is  right. 

5  to  6  should  be  a  whole  step,  i.  e.,  D  to  E  —  is  right. 

6  to  7  should  be  a  whole  step,  i.  e.,  E  to  F  —  is  wrong, 
since  E  to  F  is  only  a  ^a//"-step,  where  a  'whole  step  is 
required.     To  correct  this,  F#  is  used  instead  of  F,  giving 
the  proper  distance  from  6.     7  to  8  should  be  a  half-step, 


*  The  word  Diatonic  means  literally  "  through  all  the  tones."  Its 
applied  meaning  is,  that  one  ( and  only  one  )  note  is  to  be  written  upon 
each  degree  of  the  staff.  It  will  be  seen  later  that  the  word  is  also 
used  to  refer  to  scale-notes,  to  distinguish  them  from  notes  altered  by 
accidentals.  ( See  §  44.) 


HARMONY  SIMPLIFIED.  5 

i.  e.,  F3  to  G —  is  right.  (The  FJ  really  corrects  two 
faults,  as  without  it  the  step  7  to  8  would  have  been  too 
great. )  Expressed  in  notes  with  the  formula,  the  corrected 
scale  reads  as  follows  : — 


»^,          /^ 


In  this  way  the  pupil  should  test  each  note  in  the  following 
exercises. 

5.  In  constructing  scales,  observe  the  folio  wing  points  : 

I.  Do  not  write  two  notes  upon  the  same  degree  of 
the  staff;  e.  g.,  A  and  A$. 

n.  Do  not  skip  any  letter;  e.  g.,      /E    ^      *?      |. 
(The  letter  B  is  skipped.)  ^Er~ 


NOTE.  The  word  Scale  is  derived  from  Scala,  meaning  "  ladder." 
The  lines  and  spaces  are  used  consecutively  to  form  a  regular  series  of 
steps,  ascending  or  descending.  If  two  notes  should  be  written  upon 
one  degree  of  the  staff  (e.g.,  I),  it  would  be  necessary  to  omit  the 
note  on  the  next  degree  (e.  g.  ,  II)  to  make  up  for  it.  Such  a  method 
would  make  a  very  irregular  looking  scale  or  ladder;  t  g., 


Hi.  To  avoid  the  errors  mentioned  in  I  and  II  the 
beginner  should  always  first  make  a  skeleton,  or  outline, 
of  the  desired  scale,  i.  e.,  the  notes  only,  without  sharps 
or  flats,  writing  the  formula  of  figures  underneath.  After- 
wards he  may  bring  it  to  the  required  standard  of  steps 
and  half-steps  by  using  sharps  or  flats.  For  example  : — 


Fl*-3  life 


O 


6  HARMONY  SIMPLIFIED. 

The  next  step  is  to  "write  in  "  the  sharps  necessary 
to  make  the  notes  correspond  with  the  formula ;  thus : 

1  to  2  should  be  a  whole  step ;  a  whole  step  from  F#  is 

GJ:  therefore,  write  a  sharp  before  G. 

2  to  3  should  be  a  whole  step ;  a  whole  step  from  GJ  is 

A$ :  write  a  sharp  before  A. 

3  to  4  should  be  a  ^0//"-step ;  a  half-step  from  A#  is  B — 

is  right. 

Proceed  in  this  manner  till  the  scale  is  completed,  result- 
ing as  shown  in  Fig.  4. 


Exercises. 

6.  («.)    Construct    the    Skeleton    and    Formula,    and 
write  Major  scales  starting  from  the  following  notes :  C ; 
G;D;  A;E;B;F8;C&. 

(£.)    Construct  the  same  scales  at  the  keyboard. 

Double  Sharps. 

7.  Write  the  scale  of  Gft  as  above.     N.  B.  It  will  be 
observed  that  the  step  6  to  7,  from  E#  a  'whole  step  up- 
ward, is  not  properly  expressed  by  simply  writing  F#,  as 
that  is  only  a  ^a//"-step  from  E#.     It  is  here  necessary  to 
raise  the  FJ  another  half-step,  to  make  the  required  dis- 
tance from  E#,  which  is  done  by  using  a  double  sharp, 

written  x»  giving  "^        ^    — =[4 

*->  6  7 

Exercises, 

Write   the    scales  of  D#,   AJ,    Eft,  and  BJ,    using 
double  sharps  where  necessary.      Repeat  at  keyboard. 


HARMONY  SIMPLIFIED.  * 

The  Use  of  Flats. 

8.  Flats   are    introduced   where   without   them    notes 
would  be  a  half-step  too  high.     For  example,  in  the  scale 
starting  upon  F,  (write   it,)  the   interval  from  3  to  4  is 
a  whole  step,  while  the  formula  requires  a  half-step. 

This  is  rectified  by  the  use  of  a  flat  before  B. 

Exercises. 
Write  the  scales  of  F,  Bb,  El?,  Ab,  Db,  Gb,  and  Cb. 

Repeat  at  keyboard. 

Double  Flats. 

9.  In  the  following  scales,  double  flats,  written  bb,  will 
be  required.      From  the  foregoing,  the  pupil  should  be 
able  to  find  the  reasons  without  further  explanation. 

Exercises. 

Write  the  scales  of  Fb,   Eft?,  Ebb,  Abb,  and  Dbb. 
Repeat  at  keyboard. 

Advanced   Course. 

10.  From   a  consideration  of  the  above  it  will  be  seen,  that  in  one 
sense  there  is  but  one  Major  scale.    The  so-called  various  scales,  F, 
D,  C3,  B&,  etc.,  are  but  exact  reproductions  of  each  other,  varying  only  in 
pitch.     The  name  of  the  scale,  therefore,  merely  indicates  the  name  of 
the  starting  note  or  Keynote.     There  is  a  popular  idea  among  Piano- 
pupils  that  the  scale  of  C  Major,  having  no  black  keys,  is  the  one  per- 
feet  scale.     But  it  will  be  at  once  seen  that  the  Major  scales  are  all  alike 
in  the  manner  of  construction,  the  black  keys  upon  the  Piano  simply 
serving  to  bring  all  the  notes  of  the  scale  into  proper  relationship  with 
each  other,  i.  e.,  at  the  proper  distance  from  each  other.     For  exam- 
ple, it  should  not  be  said  that  there  is  a  wide  difference  between  the 
scale  of  C  and  the  scale  of  D^,  because  one  has  no  flats  and  the  other 
so  many.     Rather  should  it  be  said,  that  these  five  flats  serve  to  make 
the  two  scales  alike,  by   keeping  the  series  of  steps  and  half-steps 
absolutely  the  same. 

Keys. 

Regular   Course. 

11.  After  writing  a  few  scales  as  above  indicated,  the 


8  HARMONY  SIMPLIFIED. 

pupil  will  understand  that  the  notes  of  the  scale  bear  a 
certain  relationship  to  each  other.  The  starting-point  of 
each  scale  is  termed  the  Keynote ;  the  group  of  tones 
composing  the  scale,  considered  collectively,  is  called  a 

Key. 

Signatures. 

12.  Exercises.  («•)  Returning  to  the  exercises  in  §§  6 
and  8,  the  pupil  will  gather  the  sharps  or  flats  used  in  con- 
structing each  scale,  and  place  them  in  a  group  immedi- 
ately after  the  clef,  thus  forming  the  Signature  of  the  key. 

Signatures  are  a  result  of  this  uniform  construction  of  the 
scale,  and  not  the  cause  or  origin  of  the  various  keys. 

(<5.)    Recite  the  order  of  sharps  in  signatures. 
(c.)    Recite  the  order  of  flats  in  signatures. 

Circle  of  Keys  with  Sharps. 

13.  In  forming  the  key-signatures  as  above,  notice: — 
( a.  )  That  each  successive  scale  has  one  more  sharp 

than  the  one  before  it;  e.  g.,  C  has  no  sharps,  G  has  one 
sharp,  D  two,  A  three,  etc. 

14.  (b.)  That  the  note  on  the  5th  degree  of  one  scale  is 
used  as  the  first  note  of  the  next  scale;  e.  g., 

No  Sharp. 


Fig,  5. 


15.  (  c.)  This  succession  continues  till  the  note  Bjt  is 
reached.  This  note  being  the  same  as  C  natural,  we  may 
be  said  to  have  completed  the  Circle  of  Keys,  startingfrom 


HARMONY  SIMPLIFIED.  9 

C  and  continuing  till  the  same  note  ( though  called  B#  ) 
is  reached.     This  is  called  the  Circle  with  Sharps. 

16.  (  d. )  The  sharps  or  flats  of  a  signature  are  always 
written  in  the  order  in  which  they  successively  appear  in 
the  Circle  of  Keys;  e.  g.,  FJ  being  the  first  to  appear,  is 
always  written 'first, — at  the  left, —  no  matter  how  many 
sharps  there  may  be  in  the  signature.  CJ,  being  second, 
always  comes  next  to  FJJ  in  any  signature.  Written  in 
order,  and  numbered,  they  appear  as  in  Fig.  6. 


Fig.  6.*  i 


Notice,  also,  that  if  a  certain  signature  has  one  sharp, 
that  sharp  will  be  the  one  at  the  left  in  Fig.  6.  If  a 
signature  has  two  sharps,  they  will  be  the  two  at  the  left 
in  Fig.  6.  And  no  matter  how  many  there  are,  those  at 
the  left  will  always  be  included.  To  learn  the  order  in 
which  \\iejlats  appear,  observe  the  order  of  their  entrance 
ui  the  illustrations  and  exercises  in  §§  19—22. 

17.  (  e.)    It  may  be  especially  noticed,   not  only  that 
the  note  upon  the  5th  degree  is  used  as  a  starting-point 
for  the  succeeding  new  scale,  but  that  the  last  half  of 
one    scale   (  four  notes )  is  used  as  the  first  half  of  the 
next  new  one;  e.  g.,    Fig.  5.  (  See  also  §§  32  and  45.) 

18.  (y.)  But  one  note  (or  letter)  is  altered  in  passing 
from  one  scale  to  the  next  in  succession.      This  altered 
note  is  always  on  the  jth  degree,  and  is  shown  by  the 
added  sharp  appearing  in  the  Signature.** 


*  This  order  will  be  observed  by  reference  to  the  entrance  of  each  successive 
new  sharp  in  the  Exercises,  §  6. 

**  This  fact  may  be  used  to  find  the  Key  indicated  by  any  signature :  The  last 
new  sharp  being  always  at  the  right  in  the  signature,  we  may  say  that  tk* 
right-hand  sharp  is  always  on  the  yth  degree  of  the  scale.  And,  knowing  the 
7th  degree,  we  may  easily  find  the  8th  degree  or  Keynote.  (  N.  B.  The  octave 
of  the  keynote  is  the  same  as  the  keynote  itself.) 


10 


HARMONY  SIMPLIFIED. 


Circle  of  Keys  with  Flats;  Circle  of  Fourths. 

19.  A  Circle  of  Keys  using  a  gradually  increasing 
number  of  flats,  can  also  be  formed,  by  using  the  4th 
degree  of  each  scale  as  the  starting-note  (  keynote  )  of  the 
next  one;  e.  g., 

No  Flat. 
Fig.       r 


Exercises. 

20.  Write  out  the  Circle  of  Keys  with  flats,  using 
double  flats  where  necessary. 

31.  It  will  be  noticed  that  whereas  in  the  Circle  with 
sharps  the  last  half  of  each  scale  forms  the  first  half  of  the 
next,  in  flats  this  is  reversed,  the  first  half  of  one 
becoming  the  last  half  of  the  next.  (  To  understand  this, 
write  it  out  in  notes.)  The  pupil  will  further  notice, 
that  the  added  or  new  flat  will  appear  each  time  upon  the 
4th  degree.* 

22.  In  the  Circle  of  Keys  with  sharps,  the  5th  note 
of  the  scale  is  used  as  the  Keynote  of  the  following  scale. 
In  the  Circle  with  flats,  the  4th  note  is  so  used.  Now, 
counting  four  notes  of  the  scale  upward  reaches  the  same 
note  as  counting  five  notes  downward.**  Therefore,  these 
circles  are  called  the  Circle  of  Fifths,  the  sharps  counting 


*  Therefore,  to  recognize  any  key  with  flat  signature,  notice  that  the  right- 
hand  flat  is  on  the  fourth  degree  of  the  scale ;  and  to  find  the  ist  degree  or  key- 
note, count  downward  from  4  to  i. 

**  In  finding  the  fifth  below,  do  not  count  i,  2,  3,  4,  5 ;  but,  instead,  count  5, 
4, 3, 2,  i,  remembering  to  keep  the  half -step  between  4  and  3,  in  order  to  preserve 
the  correct  form  in  the  new  scale. 


HARMONY  SIMPLIFIED. 


II 


upward,  i.  e.,  by  ascending  Fifths,  anr1  the  flats  down- 
ward, i.  e.,  by  descending  Fifths. 

23.  These  circles  may  be  represented  as  follows,  the 
figures  opposite  each  key  indicating  the  number  of  sharps 
or  flats  in  the  scale : — 


Fig.  8. 

Read  around  to  the  right. 
Q 


Fig.  9. 
Read  around  to  the  left. 


N.  B.  In  finding  the  above  number  of  sharps  or  flats 
in  a  scale,  remember  that  a  Double  sharp  counts  the 
same  as  two  single  sharps. 

24.  As  the  keys  having  more  than  six  sharps  or  six 
flats  are  unnecessarily  complicated  in  notation,  it  is  cus- 
tomary to  use  the  sharp  keys  for  the  first  half  of  the  circle, 
from  C  to  FJ,  and  the  flat  keys  to  complete  the  round ; 
e.g.,  Fig.  10. 


Fig.  10. 
Read  to  right  or  left. 


In  this  way  the  change  is 
usually  made  from  F#  to  Gb, 
or  vice  versa ;  though  it  may 
be  made  at  any  point  in  the 
circle,  e.  g.,  from  G$  to  AP, 
from  Ft?  to  E,  etc.,  and  is 
called  an  Enharmonic  change 
of  key.  See  §78. 


12  HARMONY  SIMPLIFIED. 

Advanced  Course. 

25.  There  is  an  interesting  way  of  learning  the  number  of  sharps  in 
a    scale   where  there  are   more  than  six:     It   will   be  seen   at    a 
glance  that  the  key  of  C  has  no  sharps,  and  the  key  of  C$  has  seven 
sharps.     In  other  words,  each  of  the  seven  notes  has  been  raised  by 
a  sharp.     Similarly,  if  the  key  of  G  has  one  sharp,  the  key  of  G8  will 
have  i  +  7=  8,  since  each  one  of  the  notes  in  its  scale  must  be  raised 
to  change  the  key  from  G  to  G8.     Similarly,  the  key  of  D  having  two 
sharps,  the  key  of  Df  will  have  2+7  =9.     Similarly,  the  key  of  A 
having  three  sharps,  the  key  of  A8  will  have  3  +7  =  10.     Therefore,  to 
find  how  many  sharps  there  are  in  a  key  when  the  Keynote  is  written 
with  a  sharp,  simply  add  7  to  the  number  of  sharps  in  the  signature  of 
the  key  of  the  same  letter  without  the  sharp. 

26.  The  same  principle  applies  to  flat  keys  having  more  than  six 
flats ;  e.  g.,  B!>  has  two  flats  ;  therefore  Bkk  will  have  2  +  7=9  flats. 

27.  Another  interesting  point  in  this  connection  may  here  be  devel- 
oped :  — 

In  the  Circles  of  Fifths  in  §§  13-24,  the  circle  began  each  time 
with  the  key  of  C.  This  is  not  at  all  necessary,  it  being  quite  as  easy 
to  begin  upon  any  other  note  and  complete  the  circle  back  to  that  note 
again,  proceeding  in  either  direction. 

Let  the  pupil  begin  upon  G&  and  form  the  circle  by  ascending 
fifths.  This  will  decrease  the  number  of  flats  by  one  each  time  till  C 
is  reached,  after  which  sharps  will  appear  and  increase  successively. 
Vice  versa,  a  circle  can  be  constructed  beginning  upon  Fit  and  pro- 
gressing by  descending  fifths.  Notice  that  in  both  cases  the  succession 
passes  through  the  key  of  C  and  changes  from  flats  to  sharps,  or  vice 
versa,  without  altering  the  conditions  in  the  least. 

28.  From  this  it  will  be  seen  that  Flats  and  Sharps,  in  their  rela- 
tion to  each  other,  are  like  degrees  above  and  below  Zero  on  the  ther- 
mometer, sharps  being  above  and  flats  below  the  zero-mark.     Or  they 
might  be  compared  to  Positive  and  Negative  quantities  in  Algebra. 

Keyboard  and   Written  Exercises. 
Form  examples  of  the  above  mentioned  circles,  starting  in  turn 
from  CJ,  D,  D8,  E,  F,  F$,  G,  G«,  A,  Alt,  and  B,  progressing  first  by 
ascending  fifths,  and  afterward  by  descending  fifths. 

29.  Resulting  from  the  relationship  of  sharps  and  flats,  keys  are 
frequently  compared  with  respect  to  their  relative  "  sharpness,"  the 
key  having  the  fewest  flats  or  the  most  sharps  being  called  the  sharpest 
key.     Or  they  may  be  placed  in  order,  thus : — 

Cb  Gb  Db  Ab  Eb  Bb  F  C  G  D  A  E  B  FJ  Cf 
7    6    5    4    3    a    i  o  I   2  3  4  5  6   7,  and  C°mpared  by  Saying 


HARMONY  SIMPLIFIED.  13 

that  one  key  is  so  many  "  removes  "  to  the  right  ( i.  e.,  sharper)  or  left 
( i.  e.,  flatter  )  from  another  key,  counting  through  the  key  of  C  regard- 
less of  differences ;  e.  g.,  G  is  two  removes  to  the  right  from  F,  or  Bb  is 
four  removes  to  the  left  from  D.  (  See  Weitzmann's  "Musical  Theory," 
page  90.)  In  a  similar  way  the  notes  themselves  may  be  compared, 
saying  that  D  is  a  sharper  note  than  G,  since  its  key  is  represented  by 
one  more  sharp,  etc.  This  point  is  further  noticed  in  §  250. 

Exercises. 

Compare  the  sharpness  of  the  following  keys, —  i.  e.,  tell  how 
many  degrees  or  "  removes "  from  the  first  to  the  second  in  each 
pair,  and  state  which  is  the  sharper  of  the  two : — 

Keys  of  A  and  B  ;  A  and  D  ;  B  and  F«;  Ab  and  D  ;  Bb  and  AJ ; 
C  and  BJ ;  Gb  and  Ab ;  Db  and  Eb  ;  Gf  and  Ab ;  F  and  G ;  G  and  A ; 
A  and  B  ;  B  and  C. 

Exercises. 
Regular  Course. 

30.  By  means  of  the  statements  in  foot-notes  to  §§  18 
and  21,  the  pupil  should  be  able  to  recognize  at  sight  any 
key  from  its  signature  : — 

What  keys  are  represented  by   the    following    sig- 
natures ? — - 


31.  It  is  also  desirable  to  know  the  number  of  sharps 
or  flats  in  the  signature  of  a  given  key,  without  reference 
to  a  table. 

Exercises. 

Give  the  number  of  sharps  or  flats  in  the  signatures 
of  the  following  keys :  A,  Dfr,  G,  Bt>,  Ab,  D,  B,  F&, 
Gt>,  Et>,  E. 

N.  B.  If  necessary  to  do  so,  write  out  each  scale  to 
find  the  number  of  sharps  or  flats. 


14  HARMONY  SIMPLIFIED. 

Related  Keys. 

32.  Keys  having  most  notes  in  common  are  said  to  be 
related  to  each  other.     In  the  Circle  of  Fifths,  each  key  is 
related  particularly  to  the  one  before  it,  since  one  half  of 
it  is  found  in  that  scale ;  and  also  to  the  one  following, 
since  the  other  half  will  be  found  in  that  one  (  see  §  45), 
e.    g.,  the  key  of    C  is  related  to  the  key  of  G ;  also 
to  the  key  of  F.     This  subject  will  be  developed  further. 
(See  §§17  and  334.) 

Exercises. 

Name  the  two  keys  related  to  the  key  of  B :  of  F$ : 
of  D:  of  Afl:  of  Eb:  of  A:  of  Gb:  E:  DJJ. 

Facility  in  Distinguishing  the  Various 
Degrees  of  a  Key  by  Number  and  by  Name. 

33.  To  thoroughly  prepare  himselt  for  the  subsequent 
chapters,  the  pupil  should  learn  to  recognize  at  a  glance 
the  various  degrees  of  any  scale,  and  indicate  them  by 
number  or  by  name. 

Keyboard  and  Mental  Exercises. 

Placing  any  desired  scale  before  the  pupils  (for 
example,  the  scale  of  Bb),  the  teacher  should  ask  various 
questions  like  the  following :— - 

Which  degree  of  the  scale  is  Eb?  Ans.  4th  degree. 
Which  degree  of  the  scale  is  G  ?  Ans.  6th  degree. 
Which  degree  of  the  scale  is  D?  Ans.  3d  degree. 

This  exercise  should  be  carried  through  various  keys, 
and  continued  till  some  proficiency  has  been  gained.  The 
exercise  may  be  varied  by  such  questions  as  the  follow- 
ing:— 

What  is  the  2nd  degree  in  the  scale  of  A  major? 
Ans.  B. 

What  is  the  3rd  degree  in  E  major?     Ans. 


HARMONY  SIMPLIFIED.  15 

Specific  Names. 
(  To  be  learned.) 

34.  Each  Degree  of  the  scale  has  also  a  Specific  name, 
which  is  often  used  instead  of  the  number,  as  follows  :  — 
1st    degree,     Tonic. 

2d    degree,     Supertonic. 

3d     degree,     Mediant.      (  Meaning    midway  between   Tonic  ana 

Dominant.) 

4th  degree,    Subdominant. 
5th  degree,     Dominant. 

6th   degree,     Submediant.      (  Midway   between   Tonic  and   Sub- 

dominant,  when  the  latter  is 
written  below  the  former.) 

7th  degree,     Subtonic  or  Leading-Tone. 

8th  degree,    Octave  or  Tonic. 

Mental  Exercises. 

Apply  test-questions,  as  shown  in  §  33. 

Notice  that  the  prefix  "  Sub"  means  "  below,"  and 
"  Super,"  "  above  :"  e.  g.,  Supertonic  means  the  degree 
above  the  Tonic,  and  Subtonic  the  degree  below  the 
Tonic. 

The  Tonic,  Dominant,  Subdominant,  and  Leading- 
note  are  especially  important  to  know,  and  the  pupil 
should  be  able  to  find  them  'without  hesitation  in  any 

key. 

The  Minor  Scale. 

35.  It  was  noticed  that  in  the  Major  Scale  the  half- 
steps  occur  from  3  to  4,  and  from  7  to  8.     The  Minor 
Scale  is  formed  by  placing  the  half-steps  between  2  and  3, 
5  and  6,  7  and  8. 


3 


1 6  HARMONY  SIMPLIFIED. 

This  is  called  the  Harmonic  Minor  Scale,  to  dis- 
dnguish  it  from  the  Melodic  Minor  Scale,  which  has  a 
different  and  irregular  arrangement  of  the  half-steps,  as 
shown  in  Figure  12.  (  See  also  §  46.) 


r-  12.    tfe=  — ^^-^S^^^—^ 

_..-  ^^  n/^? — »-i — «J 


.42- 


«-*    -fi>-  "Cr^(5>     45678       7       654    '~      " -<S>- 
1       3N_^3  > —  ^  3^JJ       1 

36.  The  Harmonic  Minor   Scale  is  the  basis  of  the 
chords  in  the  Minor  Mode,*  while  the  Melodic  Minor 
Scale  is  generally  used  in  melodies.     It  may  be  consid- 
ered  as   a  "free "form    of  the    Harmonic    scale,  made 
necessary  by  the  fact  that  the  interval  of  i  J  steps  from  6  to 
7  in  the  Harmonic   Minor  Scale  (  see  Fig.  u)  is  rather 
unmelodious,  though  not  unmusical. 

37.  From  the  foregoing  comparison  of  the  Major  and 
Minor  scales,  the  pupil  will  realize  that  the  character  of 
a  scale  depends  upon  the  position  of  the  half -steps. 

Exercises. 

38.  Form    Harmonic   Minor    scales,    and   write    the 
figures  under  each  note  as  shown  in  Fig.  1 1 ,  starting  from 
the  following  notes :  A,  E,  B,  FJ,  Cfl,  Gtf,  Djf,  D,  G,  C, 
*',  Bt>,  Efr,  At?,  Di7. 

Relative  Minor. 

39.  Every  Major  scale  has  what  is  called  its  "Relative 
Minor,"  which  is  the  Minor  scale  having  most  notes  in 
common  with  it,  and  having  the  same  signature.     This 
Relative  Minor  is  always  founded   (  has  its  keynote,  or 
Tonic)  onthestxtfr  degree  of  the  Major  scale.     Thus, 


*  The  words  "  Major  Mode"  and  "  Minor  Mode  "  are  terms  used  when  we 
do  not  refer  to  any  particular  key,  but  wish  to  speak  of  the  character  of  Major 
or  Minor  in  a  general  way. 


HARMONY  SIMPLIFIED.  17 

the  sixth  degree  in  the  scale  of  C  is  A ;  therefore,  the 
Relative  Minor  of  C  Major  is  the  scale  (  or  key  )  of  A 
Minor.  (  In  finding  a  relative  minor,  it  may  be  easier 
for  the  pupil  to  look  for  the  keynote  I  \  steps  below  rather 
than  the  sixth  above,  the  result  being  the  same.) 

Exercises. 

Find  the  Relative  Minor  ( and  write  the  proper  sig- 
nature) of  C  Major;  of  G,  D,  A,  E,  and  B  Major;  of  F, 
Bt>,  Eb,  Ab,  Db  Major. 

40.  Correlatively,  each  Minor  has  its  Relative  Major? 
which  is  found  on  the  third  degree  of  the  Minor  scale. 
For  example,  the  relativ-r  major  of  A  Min^r  is  C  Major. 
In  other  words,   A  Minor  is  the  relative  Minor  of  C 
Major ;  and  C  Major  is  the  relative  Major  of  A  Minor. 

Mental  Exercises  and  Drill. 

Find  the  Relative  Majors  of  the  following  Minor 
scales :  A,  E,  B,  F&  Ctf,  Gtf,  Dtf,  D,  G,  C,  F,  Bb,  Eb, 
Ab,  Db. 

Signatures  in  Minor. 

41.  The  pupil  will  notice  that  the  Relative  Minor  of 
any  Major  scale  has  the  same  notes  as  the  latter,  except- 
ing the  seventh  degree,  which  is  raised  by  an  accidental. 
For  example,  A  Minor  has  the  same  notes  as  C  Major, 
excepting  the  G#.     This  accidental  raising  of  the  seventh 
degree  is  caused  by  the  fact  that  the  seventh  degree,  or 
"Leading-tone,"  should  be  only  a  half-step   distant  from 
the  Tonic.      (  See  §  46.) 

In  collecting  the  sharps  or  flats  to  form  the  signature 
of  a  minor  key,  this  fact  should  be  considered : —  The 
accidental  found  before  the  seventh  degree  does  not  be- 
long to  the  signature. 


X8  HARMONY  SIMPLIFIED. 

Exercises. 

Write  the  signatures  of  the  following  Minor  keys, 
proceeding  as  directed  in  §12:  A,  E,  B,  FJ{,  CJ,  GJf, 
Dtf,  D,  G,  C,  F,  Bb,  Eb. 

The  Circle  of  Keys  in  Minor. 

42.  The  Circle  of  Fifths  can  be  made  with  Minor  keys 
as  well  as  with  Major. 

Exercises. 

(a.)  Form  the  Circle  with  sharps,  beginning  with 
the  key  of  A  Minor. 

( <5.)  Form  the  Circle  with  flats,  beginning  with  the 
key  of  A  Minor. 

(c.)  Form  the  Circle  beginning  upon  various  other 
notes. 

The  Chromatic  Scale. 

43.  When  the  half-steps  lying  between  the  notes  of  the 
Diatonic  scales  are  included,   thus  producing  a  scale  of 
half-steps  exclusively,  it  is  called  a  Chromatic  scale.     It 
\s  customary  to  use  sharps  in  writing  the  intermediate 
h«lf-steps  in  an  ascending  chromatic  scale,  and  flats  in 
the  descending  scale ;  e.  g., 


Chromatic  Alteration. 
44.  When  a  note  is  raised  or  lowered  a  half-step  by 


HARMONY  SIMPLIFIED. 


an  accidental,  consequently  'without  changing  its  post' 
tion  upon  the  staff,  it  is  said  to  be  chromatically  altered ; 

e.  g. 

A  Chromatic  Half-Step  is  one  expressed  upon  ont 
degree  of  the  staff;  e.  g.,  A  —  Aft. 

A  Diatonic  Half-Step  is  one  expressed  upon  two 
degrees  of  the  staff;  e.  g.,  A — Bfr. 

In  general,  a  Diatonic  progression  is  one  where  the 
letter  is  changed  in  the  succession  of  notes  ;  and  a  Chro- 
matic progression  is  one  where  the  letter  is  not  changed, 
but  altered  by  the  use  of  an  accidental. 

At  the  close  of  each  chapter  the  pupil  should  make 
a  synopsis  of  the  principal  facts  contained  therein,  class- 
ifying and  arranging  them  in  order.  The  following 
table  is  intended  to  assist  the  pupil  in  this. 

Synopsis  of  Chapter  I. 

'  Formula : —  Half-steps  3-4  and  7-8. 
Keys. 
Signatures. 
Circle  of  Fifths:  Ascending. 


Scales : 


Major : 


Relative  Keys : 


\  Descending. 
Fifth  above,  or  Dominant. 
Fifth  below,  or  SubdominanL 
Relative  Minor. 


Specific  Names. 
Major  scales  all  alike. 


Minor ; 


Chromatic : 


Formula  : 


Harmonic;    Half-steps,  2-3,    5-6, 

7-8. 
Melodic;  Half-steps,  up,  2-3, 

7-8 :  down,  6-5,  3-2. 
Relative  Major. 

j  Same   as  Relative  Major. 
'"  '•  \  Omit  sign  of  raised  Leading-note. 
Leading-note  raised  by  an  accidental. 

Position  of  half-steps. 
Notation. 


20  HARMONY  SIMPLIFIED. 

Historical. 

45.  The  Modern  Scale  is  a  gradual  development  from 
the  ancient  Greek  Modes,  in  which  the  semitones  occu- 
pied varying  places  in  the  scale,  according  to  the  mode. 
See  Grove's  "Dictionary  of  Music  ;"  Vol.  II,  p.  341,  and 
Baker's  "New  Dictionary  of  Musical  Terms;"  p.  88  et 
seq.  The  Major  Scale  may  be  considered  as  composed 
of  two  Tetrachords,*  placed  one  above  another;  e.  g., 

CDEF  GABC 


Tetrachord.  Tetrachord. 

Until  the  I3th  century,  the  use  and  influence  of  the 
semitones  in  Music  were  not  fully  realized;  therefore, 
in  the  music  previous  to  that  time,  we  find  (  according 
to  modern  standards  )  a  lack  of  Tonal  feeling,  or  sense  of 
being  in  some  particular  key.  In  the  time  of  Palestrina 
it  became  customary  to  sing  the  seventh  degree  as  if  it 
were  only  a  half-step  from  the  eighth,  although  this  was 
contrary  to  the  notation,  showing  the  need  of  something 
beyond  the  scales  then  in  use. 

In  the  seventeenth  century  the  modern  scale  began 
to  displace  the  Gregorian  Modes ;  the  sharps  and  flats, 
instead  of  being  dispersed  through  the  composition  or 
left  to  the  discretion  of  the  performer,  were  gathered  to- 
gether to  form  the  signature ;  the  dividing  lines  between 
the  keys  were  thus  more  distinctly  marked ;  and  Modern 
Music,  as  opposed  to  the  Ancient  Modes,  soon  made  a 
distinct  place  for  itself. 

46.  The  oldest  form  of  the  Minor  scale  was  as  shown 
in  Fig.  14. 


•  A  Tetrachord  is  a  scale  of  four  notes,  having  one  half-step.    Tetrachordi 
belonged  to  the  musical  system  of  the  ancient  Greeks. 


HARMONY  SIMPLIFIED. 


21 


Flg.  1 4. 


I 


4331 


As  the  feeling  of  Tonality  developed,  a  "  Leading- 
note  "  was  demanded  which  should  point  more  decidedly 
toward  the  Keynote,  and  thus  impart  a  greater  feeling  of 
satisfaction  when  the  final  chord  was  reached.*  Thus 
the  yth  degree  of  the  scale  was  raised  by  an  accidental, 
giving  the  form  as  in  Fig.  15,  which  is  seen  to  be  our 
present  Harmonic  Minor  scale. 


FI..15.H& 


3       3      4 


4331 


This  form  leaves  an  interval  of  i  J  steps  between  the 
6th  and  7th  degrees;  and  for  the  sake  of  a  smoother 
effect  it  became  customary  to  raise  the  6th  degree  also  a 
half-step,  where  the  harmony  would  allow  it,  giving  the 
form  shown  at  ( a ),  Fig.  16,  which  is  our  present 
Melodic  Minor  scale. 


(a.) 


(b.) 


Fig.  16. 


y 

^_,    ^^  *f-^  "" 

W         °    fD    ^                 U 

/f 

H5—  2ZZ2 

°  r3 

|(TV 

& 

™^ 

&  oil 

Vly 

11 

A  "  Leading-note ''  being  unnecessary  in  a  descend- 
ing scale,   the  two   notes   raised  by  accidentals  in    the 


*  The  need  of  a  "  Leading-note  "  to  give  the  feeling  of  satisfaction  when  the 
final  chord  is  reached,  is  shown  by  comparing  (a )  and  ( b )  in  Fig.  17. 

(a.)  (b.) 


Fig.  1  7. 


7         S3  ~l   fay         ^>      ¥1 

^ra — ^9 • — ff— >^ — 49 *-* 


22  HARMONY  SIMPLIFIED. 

ascending  scale  are  usually  restored  in  descending 
[(<5),  Fig.  1 6],  giving  the  complete  Melodic  minor 
scale  now  used. 

Exercises  in  Musical  Dictation,  for  the  Develop- 
ment of  the  Perceptive  Faculties. 

47.  If  we  would  rightly  understand  Music,  it  is  indispensable  that 
we  become   able  to  recognize  what  we  hear,  just    as  we   recognize 
printed  words  upon  first  sight. 

The  reason  so  few  have  the  faculty  of  listening  intelligently,  is 
not  that  it  is  difficult,  but  because  little  or  no  attention  has  been  paid 
to  this  most  important  subject.  Briefly  summed  up,  the  steps  of  the 
process  of  development  consist  in  gaining  the  power :  — 

1.  To  distinguish  Half-steps  from  Whole-steps. 

2.  To  distinguish  the  various  notes  of  the  scale. 

3.  To  distinguish  Intervals. 

4.  To  distinguish  the  Major  from  the  Minor  Mode. 

5.  To  distinguish  Chords  and  their  inversions,  and  to  realize  their 
position  in  the  key. 

6.  To  trace  simple  Modulations. 

7.  To  distinguish  the  Divisions  of  Time,  Rhythm,  etc. 

8.  To  note   the  various  features  of  Form,  learning  to  recognize 
Motives,  Themes,  succession  of  keys,  Periods,  and  the  general  plan 
of  construction. 

9.  To  be  able  to  express  all  of  the  above  in  Musical  Notation.  * 

By  taking  this  study  step  by  step,  and  in  connection  with  the 
study  of  Harmony,  there  will  be  added  interest  in  the  latter  by  reason 
of  the  ability  to  apply  each  point  as  soon  as  learned.  There  will  also 
be  a  deeper  and  more  practical  comprehension  of  Harmony,  and  a 
more  intelligent  knowledge  of  Music  as  an  Art  and  a  Science. 

To  Distinguish  Notes  of  the  Scale. 

48.  (a.)  First  teach  the  pupils,  by  experiment  and  careful  concen- 
tration in  listening,  to  distinguish  between  Half  and  Whole  steps  in 
both  upward  and  downward   progression.     This  may  occupy  parts 
of  six  or  eight  lessons. 

(6).  The  best  and  only  really  successful  manner  of  teaching  the 
notes  of  the  scale  and  how  to  distinguish  them,  is  through  the  medium 
of  the  voice.  The  foundation  of  the  musical  perceptions  lies  in  the 
possession  of  a  "working  "  knowledge  of  the  Major  scale.  The  first 

*  The  above  represents  the  complete  process,  facility  in  all  of  which  is 
attained  only  by  gifted  minds.  But  a  moderate  degree  of  proficiency  is  within 
the  reach  of  any  one  possessed  of  ordinary  perserverance. 


HARMONY  SIMPLIFIED.  23 

step  is  therefore  to  thoroughly  practise  singing  the  majoi  scale,  using 
the  syllables  Doh,  Ray,  Me,  Fah,  Soh,  Lah,  Te,  Doh1.*  This  should 
be  continued  till  the  pupils  can  skip  from  any  degree  to  any  other,  and 
can  also  recognize  the  same  when  sung  or  played  by  the  teacher. 

(f.)  In  connection  with  the  above,  the  teacher  should  sing,  or  play 
the  ascending  and  descending  scale,  while  the  class,  provided  with  a 
book  of  score-paper,  write  each  note  as  it  is  sung.  During  this 
exercise  (  of  writing,  or  musical  dictation  )  the  teacher  should  frequently 
ask,  "  What  was  the  last  note  sung  ?"  requiring  as  an  answer  the  name 
of  the  syllable,  Doh,  Ray,  etc. 

49.  (</.)  The  scale  may  now  be  broken  up;  for  example,  going  up  a 
few  notes  and  coming  down  part  way ;  then  going  up  a  little  further, 
etc.,  taking  care  to  have  all  the  progressions  diatonic,  —  i.  e.,  no  skips, 
and  no  notes  altered  by  accidentals.  ( The  pupils  should  write  these 
notes  as  sung  or  played.) 

(/. )  Afterward,  simple  skips  (3ds,  4ths,  and  5ths)  may  be  inter- 
spersed, always  keeping  enough  of  the  diatonic  progression  to  retain 
the  feeling  of  tonality,  and  taking  care  to  increase  the  difficulty  very 
gradually. 

These  exercises  must  be  practised  thoroughly,  in  order  to  lay  the 
foundation  for  the  more  difficult  subsequent  studies.  The  keys  in 
which  these  dictation-exercises  are  written,  should  be  frequently 
changed  during  a  lesson,  that  all  keys  may  become  familiar.  It  i& 
not  necessary  that  the  teacher  should  play  in  a  different  key  when 
the  change  is  made.  He  may  simply  say,  striking  any  note  on  the 

Piano  :  "  This  note  is  Doh  :  write  in  the    key  of  ,"  After  a  time 

he  may  say  :  "  Now  write  in  the  key  of  '  mentioning  any  key  he 

may  desire.  Thus  the  pupils  will  become  able  to  express  themselves 
in  one  key  as  easily  as  in  another,  and  will  realize  that  the  great  point 
is  the  relationship  of  the  sounds  rather  than  the  actual  notes. 

50.  Although  the  ability  to  sing  any  succession  of  tones  may  not 
appear  very  requisite  for  the  first  exercises,  it  will  be  found  in  the  sub- 
sequent studies  in  recognizing  chords,  modulations,  etc.,  that  the 
highest  possible  development  of  this  power  is  of  great  advantage. 
Therefore,  the  practice  of  singing  the  scale  and  skipping  about  in  it 
should  be  continued  for  some  time.  A  diagram  like  Fig.  18,  written 
on  a  wall-chart,  is  best  for  the  first  practice. 


*  The  use  of    syllables  is  helpful  in  establishing  the  relationship  of  t&e 
various  notes  to  each  other. 


24  HARMONY  SIMPLIFIED. 

Fig.  18. 

Fah1  51.  Besides  practice   in  singing  different  tones,  the  pupS 

Me1  should  be  exercised  in  thinking  how  a  succession  of  notes 
Ray1  would  sound.  For  example,  taking  a  short  succession 
DOH1  like 

TE  A  or:  _  or: 

LAH        Flg>  ,  £ 
SOH 
FAH 

ME  the  pupil  should,  by  remembering  the  syllabic  names  of 
RAY  the  notes  and  the  sounds  connected  with  those  names,  try 
DOH  to  think  how  the  passage  would  sound,  afterward  compar- 
Te(  ing  with  the  effect  when  sung  or  played. 

Lah, 

Soh,  52.  While  exercising  the  pupil  on  Pitch,  studies  in  Rhythm 
should  be  given,  by  means  of  notes  of  various  lengths,  suc- 
cessions of  notes  with  rhythmic  flow,  etc.  Rests  should  also  be  intro- 
duced. The  inexperienced  will  find  material  for  such  exercises  in  any 
book  on  Sight-singing  or  Musical  Dictation. 

Specimen  Test  Questions. 

Illustrating  the  Drill  which  should  be  given  at  the  end  of  each 
chapter.  —  Additional  questions  upon  this  and  other  chapters  may  be 
found  in  the  author's  Key  to  '•'•Harmony  Simplified";  also  answers 
for  all  questions  and  exercises  in  this  book. 

1.  Where  are  Half  steps  in  the  Major  Scale  ?     State 
two  or  three   foundation   principles    covering  its   con- 
struction. 

2.  For  what  are   Sharps   and    Flats  used?*     Also 
Double  Sharps,  and  Double  Flats  ? 

3.  How  many  kinds  of  Major  scales  are  there,  and 
why  ? 

4.  What  is  a  Signature  ?  *     Give  its  origin.  * 

5.  Describe  Tetrachords  and  their  office  in  the  Order 
of  Keys.  * 

6.  Give    the  Order  of    Scales  with   Sharps.      Also 
with  Flats. 

*  But  few  reach  the  underlying  thought  in  tnese  questions. 


HARMONY  SIMPLIFIED.  25 

7.  What   is  the   difference  between    a    Scale   and   a 
Key  ?  * 

8.  What  is  the  difference  between  the  Harmonic  and 
Melodic  Minor  ? 

9.  Name  the    Keys    related    to   G    Major    and    give 
reasons  therefor. 

10.  How  would  you  discover  a  key  from  the  Signa- 
ture in  Sharps  or  Flats  ? 

1 1 .  What  is  the  Signature  of  any  Minor  Key  ? 

12.  What  is  the  office  of  the  Half-step  in  scale  con- 
struction ?  * 

13.  Why  is   there  an  accidental   in   every   Harmonic 
Minor  scale  ? 

14.  Was  it  there  originally  ? 

15.  How  would  you  change  a  Major  to  its  Tonic  Minor 
key,  or  vice  versa  ?  * 

1 6.  What  do  you  understand  by  the  term  "  Tonality  "  ? 
How   is   it   developed,    and    how    does    it    differ    from 
"  Key  "  ?  * 

NOTE.  The  more  obvious  questions  are  here  omitted,  but 
should  be  included  by  the  teacher,  and  possibly  used  to  "  lead  up  to  " 
these  questions. 

NOTE.  The  author  introduced  into  his  own  work  a  system  of 
Daily  Drill  upon  each  subject  as  it  was  completed  in  the  course  of 
study.  The  suggestion,  it  is  hoped,  will  prove  of  as  great  value  to 
others  as  it  has  proved  in  his  own  experience.  Such  drills  may  be 
found  in  the  Key  and  Graded  Lessons. 


CHAPTER  II. 

INTERVALS. 

SPECIAL  NOTE.  —  On  taking  up  this  subject,  it  is  well  to  observe 
that  it  is  divided  into  four  general  sections,  which  at  first  are  studied 
rather  independently  of  one  another,  viz. :  The  Names  of  Intervals; 
the  Specific  Names ;  Inversions ;  and  Consonant  and  Dissonant 
Try  to  keep  these  four  lines  of  study  distinct  in  the  mind. 

*  These  questions  are  designed  to  stimulate  original  thought. 


26  HARMONY  SIMPLIFIED. 

53.  An  Interval  in  Music  is  like  an  interval  anywhere 
else,  —  it    is    an    expression    of  distance   between    two 
things.      Consequently,  it  may  be  defined  as  the  distances 
or  difference  in  pitch,  between  two  given  tones.* 

54.  An  Interval  may  be  formed  by  two  notes,  eithei 
sounded  together,  or  in  succession.  — 

(a.)  is  called  an  Harmonic 
Interval. 

is   called    a    Melodic 
Interval. 


General  Names  of  Intervals. 

55.  An  Interval  is  named  according  to  the  number  of 
degrees  of  the  scale  included  in  its  extent. 

Thus,  the  Interval  from  C  to  D  *  *  is  called  a  2nd, 
because  two  Degrees  of  the  scale  are  concerned  in  its 
production.  Similarly,  from  C  to  E  is  a  3rd,  from  C  to 
F  a  4th,  from  E  to  B  a  5th,  etc. 

56.  To  determine  the  name  of  an  interval,  count  the 
degrees,   including  those    upon  which  the  notes  of  the 
interval  stand  (i.  e.,  including  extremes).     For  example, 


in  determining  the  name  of     (fl^   &  ",  count  the  degrees 

*->    ~-<9- 

upon  which  C  and  A  stand,  as  well  as  those  lying 
between,  giving  the  total  of  six  ;  therefore,  the  interval 
in  question  must  be  a  6th.  N.  B.  Unless  otherwise 
indicated,  intervals  are  usually  counted  from  the  lower 
note  upward 


Advanced  Course. 

*  The  word  Interval  may  also  mean  the  relationship  of  two  notes  in  respect 
to  pitch ;  or  the  effect  produced  by  the  two  notes  sounding-  together  or  in  suc- 
cession. 

*  *  The  fow*r  note  of  an  interval  or  chord  Is  always  mentioned  first. 


HARMONY  SIMPLIFIED.  27 

Table  of  Intervals. 


Pig.  21. 


_-  -  -          --    --    --    --    --    --    -- 

Unison     2d.     3d.     4th.   5th.    6th.    ;th.  8th.    gth.  loth. 
or  Prime.* 

Keyboard  and  Written  Exercises.** 
57.   (a.)  Form  tables    similar  to    the    above,  starting 
from    the  notes  D,  F,  E,   G,  B,  and  A  (all  in  the  key 
of  C). 

(£.)   Form  similar  tables  in  the  keys  of  G,  F,  D, 
Bfr,  etc. 

(c.)    Write  all  the  Seconds  in  the  key  of  G  ;  e.  g. 


FIR.  22. 


etc. 


(d.)  Write  all  the  Thirds  in  the  key  of  F. 

(e.)  Write  all  the  Fourths,  Fifths,  Sixths, 
Sevenths  and  Octaves  in  the  key  of  E  ;  in  the  key  of  Bfr ; 
A;  Db;  Fj. 

(f.)   Repeat  all  of  the  above  at  the  keyboard. 

Specific  Names  of  Intervals. 

58.  Intervals  are  of  various  kinds,  the  names  of  which 
fairly  express  their  meaning,  as  follows  :  — 

Major  :      ?  »  *  *    The  normal  or  standard  of  measure- 
Perfect :    j         inent.    The  difference  between  the  two 
will  be  explained  in  §  §  60,  73  and  76. 

*  When  two  voices  sound  the  same  note,  there  is  no  difference  in  pitch, 
and  therefore  no  interval  between  them.    Consequently,  the  Unison  cannot 
strictly  be  called  an  interval. 

*  *  Pupils  are  liable  to  make  mistakes  when  counting  an  interval  upon 
the  keyboard  ;  but  when  written,  by  counting:  the  lines  or  spaces  upon  which 
the  notes  stand  and  all  the  intervening  lines  and  spaces,  mistakes  become 
impossible.    Or  better  still,  count  the  number  of  letters  involved,  including 
extremes. 

*  *  *  For  the  present  the  pupil  need  only  know  that  Unisons,  Fourths, 
Fifths  and  Octaves  may  be  Perfect,  but  not  Major.     (Some  theorists  call  the 
Perfect  intervals  Per/erf  Major,  \g  distinguish  them  from  those  which  are 
limply  Major.) 


28  HARMONY  SIMPLfflED. 

Minor:    meaning  "less"  by  a  semitone  than  Major. 

Diminished:  meaning  still  less,  or  less  by  a  semitone 
than  Minor  or  Perfect. 

Augmented:  meaning  increased,  or  greater  by  a  semi- 
tone than  Major  or  Perfect. 

The  difference  between  the  various  kinds  of  intervals  is  illus- 
trated by  the  following,  from  Eugene  Thayer: — '  Let  us  take  a  pair 
of  hand-bellows,  and  allowing  them  to  take  their  natural  position, 
find  them  to  be  nearly  wide  open  —  the  handles  well  apart.  Let  this 
position  represent  the  Major  interval.  If  the  upper  handle  be  pressed 
down  a  little,  the  distance  between  the  two  handles  (or  the  interval) 
is  lessened  :  —  this  corresponds  to  the  Minor  interval.  If  we  now 
raise  the  lower  handle,  pressing  them  still  nearer  together,  the  dis- 
tance (interval)  is  again  decreased,  representing  a  Diminished  interval. 
Again,  letting  the  handles  spring  back  to  their  original  (normal)  posi- 
tion, representing  the  Major  interval,  if  we  raise  the  upper  handle,  or 
depress  the  lower  one,  we  increase  the  distance  between  them,  thus 
representing  an  Augmented  interval.' 

The  Standard  of  Measurement. 

59.  Consider  the  scale  of  C  upon  the  keyboard. 
From  C  to  any  other  degree  of  the  scale  of  C,  or  from  C  to  any 
white  key  upon  the  Piano,  is  a  Major  or  Perfect,  i.  e.,  a  Normal, 
interval. 

(  For  example,  see  Fig.  21.  All  the  intervals  there 
given  are  Major  or  Perfect.)  This  gives  us  a  practical 
standard  of  measurement  by  which  ive  can  measure  any 
interval;  for,  as  we  have  seen  in  the  above  definitions, 
a  Minor  interval  is  a  semitone  smaller  than  a  Major,  an 
Augmented  a  semitone  larger  than  a  Major,  etc. 

60.  Of  the  Normal  Intervals  (as  shown  in  Fig.  21)  the  Unison, 
Fourth,  Fifth,  and  Octave  are  called  Perfect ;  while  the  others,  namely, 
the  Second,  Third,  Sixth  and  Seventh,  are  called  Major.  The 
same  statement  in  more  general  terms  would  be,  "  Normal  Unisons, 
Fourths,  Fifths  and  Octaves  are  called  Perfect ;  while  Normal 
Seconds,  Thirds,  Sixths  and  Sevenths  are  called  Major."  Still 
another  form  of  the  statement  is,  "  The  Normal  intervals  are  divided 


HARMONY  SIMPLIFIED.  39 

mto  two  classes,  half  of  them  being  called  Perfect  and  half  Major." 
Memorize  the  first  statement  above,  and  do  not  seek  to  understand 
the  reason  for  the  above  divisions  until  you  study  the  Inversions. 
The  reasons  will  become  more  apparent  as  you  go  into  the  subject. 

61.  It  is  not  the  mere  elevation  or  depression  of  the 
notes  that  changes  an  interval,  but  the  fact  that  the  tones 
are  either    separated   further  from    each    other,  or  are 
brought  nearer  together;  i.  e.,  the  distance  is  changed. 

62.  Let  us  make  a  practical  application  of  the  above. 
We  found  in  §  56,  that  from  C  to  A  (counting  up- 
ward)  is  a  Sixth ;  and,  according  to  §  59  and  foot-note, 


it  is  a  Major  Sixth  : 


Let  us  apply  some  of  the  changes  mentioned  in  §  58 
to  this.     Lowering  the  upper  note  a  semitone,  we  have 


;,  which,  being  a  semitone  less  than  the  Major 

Sixth,  is  called  a  Minor  Sixth. 

Again,  taking  this  Minor  Sixth,  by  again  decreasing 
the  distance  between  the  notes,  this  time  raising  the 
lower  note  by  prefixing  a  sharp,  we  obtain  a  Diminished 

Sixth :  * 

Again,  returning  to  the  Major  Sixth  as  a  starting- 
place,  if  the  upper  note  be  raised  a  half-step,  the 
distance  between  the  two  notes  will  be  increased, 

forming  an  Augmented   Sixth :   F((T)    fl1^       '- 
See  also  "  Key,"  §  62. 


Exercises. 
Name  each  of  the  following  intervals. 


%5>- 


*The  interval  of  the  Diminished  6th  is  not  commonly  used  (see  Table, 
$  64),  but  it  is  useful  here  for  Illustration. 


30  HARMONY  SIMPLIFIED. 

Exact  Measurement  of  Intervals. 

63.  An  interval  can  be  exactly  measured,  and  its  Spe- 
cific name  placed  beyond  doubt,  by  counting  the  num- 
ber of  Half- Steps  contained  in  it  (just  as  we  counted  the 
number  of  degrees  to  obtain  the  General  name).     For 
example,  from  C  to  A  is  a  6th.      Counting  the  number 
of  half-steps,  we  find  it  has  nine.     Therefore,    as   our 
Standard  Sixth  contains  nine  half-s*:eps,  any  other  Afajor 
sixth,    without   regard    to  its    position,   must  have   the 
same   number  of  half-steps.     According    to    §    58,   an 
Augmented  Sixth  must  have  one  half-step  more,  or  ten 
half-steps  :  and  a  Minor  Sixth  one  half-step  less,  or  eight 
half-steps.     In  this  way  we  may  compare  any  interval 
with  the  Standard  of  Measurement,  and  learn  whether  it 
is  Major,  Minor,  Diminished,  or  Augmented. 

64.  As  no  interval  is  commonly  used  in  more  than 
three  of  these  forms,  a  table  is  subjoined,  showing  them 
in  order  as  generally  used. 

Table  of  Intervals. 

Showing  the  number  of  ^#^"-steps  in  any  interval- 
[  For  reference ;  —  not  to  be  memorized.*] 

Diminished.  Minor.          Perfect.    Major.  Augmented. 
—  o  —  I 

I  2  3 

3  4  — 

5  * 

-               7  -  8 

8             —  9  10 

10             —  ii  — 

12  —  — 

—           13             —14  15 

*  It  is  unnecessary  to  memorize  this  table,  as  the  pupil  can  easily  find  the 
number  of  half-steps  in  a  given  interval  by  the  use  of  the  principles  shown  in 


Primes  : 

— 

Seconds  : 

— 

Thirds  : 

2 

Fourths  : 

4 

Fifths: 

6 

Sixths  : 

— 

Sevenths  : 

9 

Octaves  : 

ii 

Ninths  : 

— 

HARMONY  SIMPLIFIED.  31 

65.  In  working  out  the  following  exercises,  the  pupil 
jhould  first  find  the  note  for  the  General  name  of  the 
interval  as  shown  in  §  56,  afterward  adding  any  sharps  or 
flats  necessary  to  bring  it  into  correspondence  with  the 
requirements    of    the     Specific    name.     For    example, 
"What   is   the   Major    Sixth   from    E?"     Process:  — 
Beginning  to  count  with  the  note  E,  the  sixth  count  will 
bring  us  to  C ;  therefore,  a  Sixth  from  E  must  be  C ;  C  is 
thus  the  General  name  for  the  desired  interval.     Next, 
a   Major  Sixth   must    have    (refer   to    the    standard   of 
measurement)   nine    half-steps :  as  there   are   but  eight 
half-steps  from  E  to  C,  it  is  evident  that  the  latter  must 
be  raised  by  a  sharp,  giving,  for  the  Major  Sixth,  C#. 

Advanced   Course. 

66.  The  standard  of  measurement,  §  59,  showed  the  intervals  from 
the  note  C  to  every  other  note  in  the  scale  of  C  to  be  "  Normal  "inter- 
vals.     In  a  similar  way,  from  the  Keynote  of  any  other  key  to  any  note 
of  that  scale  would  be  also  a  "  Normal  "  interval,  e.  g.,  from  A&  to  any 
note  in  the  scale  of  A^  would  be  just  as  "  normal  "  as  from  C  to  any 
note  in  the  scale  of  C.     Therefore,  instead  of  counting  the  half-steps 
in  naming  or  forming  a  specific  interval,  the  practised  musician  would 
think, "  What  is  the  '  Normal '  interval  ?"  counting  from  any  given 
note  (by  transferring  his  thought  for  the  instant  to  the  key  of  that 
given  note),  and  would  raise  or  lower  that  normal  note  to  obtain  the 
required  interval.     For  example :  What  is  the  Augmented  Sixth  from 
FJ  ?       Process :  —  If  we  were  in  the  key  of  F$,  the  Normal  Sixth 
would  be  found  by  counting  up  to  the  6th  degree  of  the  scale,  giving 
the  note    D8.     (Having  found    the  desired  interval,    do    not   think 
further  in  the  key  of  Fjf.)     As  the  required  Augmented  Sixth  is  a 
half-step  greater  than  the  Normal,  the  Df  must  be   raised  another 
half-step,  giving  the  note  DX  (double  sharp). 

Regular   Course. 

67.  Remember  that  the  General  name  is  obtained  by 
counting  the  degrees  of  the  scale,  while  the  Specific 
name  is  found  by  counting  the  half-steps.  Therefore, 


32  HARMONY  SIMPLIFIED. 

the  use  of  sharps  or  Jlats  can  never  change  the  General 
name  of  an  interval ;  —  a  Sixth  remains  a  Sixth  even  if 
there  are  several  sharps  or  flats  prefixed.  The  kind  of 
Sixth  it  would  be  is  quite  a  different  question,  coming 
under  the  head  of  Specific  name. 

Exercises. 

68.  (a.)  Form  a  Major  Sixth  from  each  of  the  follow- 
ing notes,  counting  upward:  — D,  E,  F$,  B,  A,  Bb,  Ab, 
Db,  Aft,  G,  Eb,  Gb,  Cb,  Git,  CB,  Fb,  BJ,  etc. 

(<5.)  From  the  same  notes,  form  Major  Thirds, 
Minor  Thirds,  and  Minor  Sevenths. 

(c.)  Form  Diminished  yths  from  D,  E,  FJ,  B,  A, 
Bb,  Ab,  AJt,  C,  Eb,  Gft  CJf,  BJt,  etc. 

(a?.)  Form  Augmented  4ths  from  D,  E,  F#,B,  A, 
Bb,  Ab,  Db,  Atf,  Gtf,  Eb,  Gb,  Cb,  G*,  Of,  Fb,  etc. 

NOTE.  In  accidentally  raising  or  lowering  a  note,  it  is  not  custom- 
ary to  raise  or  lower  it  beyond  the  pitch  of  the  natural  next  above  or 
below  ;  e.  g.,  B  would  not  be  double-sharped,  since  that  would  bring 
it  beyond  C,  the  next  natural ;  nor  would  F  have  a  double  flat,  since 
that  would  take  it  beyond  the  next  natural. 

(e.)  Repeat  all  of  the  above  at  the  keyboard. 

Extended  Intervals. 

69.  As  an  octave  above  any  note  is  considered  a  repe- 
tition of  that  note  and  bears  the  same  name,  so  intervals 
(with  the  exception  of  the  Ninth),  if  they  extend  over 
more  than  an  octave,  are  considered  as  repetitions  of  the 
smaller  intervals   formed  by  Ihe  same  notes  an  octave 


nearer  together.     Thus :  I  (fl\  which  is  an  interval 

of  an  Eleventh,  is  considered  as  an  extension  of  G 


HARMONY  SIMPLIFIED.  33 

which  is  a  Fourth.      Therefore,   in  rinding  intervals,  the 
notes  should  be  brought  within  the  compass  of  an  octave. 

Exercises. 

Name  the  following  intervals,  lowering  the  upper 
note,  or  raising  the  lower,  one  or  two  octaves : 


O  -,51-          "         " 

-^      -vr     -    ^ 
The  interval  of  a  Ninth  is  usually  not  contracted  in 
this  way,  as  the  chord  of  the  Ninth  requires  that  interval 
to  be  nine  degrees  from  the  root.     See  Chapter  VIII. 

Inversion  of  Intervals. 

70.  By  Inversion  of  Intervals  is  meant  that  the  notes 
change  their  relative  positions  ; —  the  upper  one,  by  being 
lowered  an  octave  (retaining  its  original  name) ,  becom- 
ing lower  than  the  other ;  or,  the  lower  one,  by  being 
raised  an  octave,  becoming  higher  than  its  fellow.  Thus, 
the  interval  at  (a)  in  the  accompanying  figure  becomes 
like  (3)  by  lowering  the  upper  note,  and  like  (c)  by 
raising  the  lower  one,  which  is  the  same  thing  as  (3), 
but  an  octave  higher. 

(a.)       (6.)        (c.) 


Keyboard  and  Written  Exercises. 

Invert  the  following  (a)  by  lowering  the  upper  note 
one  octave ;  (b)  by  raising  the  lower  note. 


1 


71.  Subjoined  is  a  Table  showing  a  few  intervals  in- 
verted. The  lower  staff  shows  the  result  of  inverting  the 
intervals  contained  in  the  upper  staff.  Notice  that  in  the 


34 


HARMONY  SIMPLIFIED. 


tables  the  inversions  are  produced  by  raising  the  lower 
note  one  octave.  It  would  have  been  quite  as  easy  to 
lower  the  upper  notes  one  octave,  writing  the  inversions 
in  the  Bass  clef.  The  quarter-notes  in  the  lower  staff 
show  the  notes  which  have  been  raised  an  octave. 


Fig.  23. 


-y- 





1                                                     1 

i?H 





1  1 

Saz 

I 

I               f3                               \ 

_Q- 

-ee-             is^ 

Prime                Seco 
becomes           becon 

1 

tid               Third 
ics            becomes 

1 

Fourth 
becomes 

,         1 

sE  —  *         i    *         i    * 

EEE 

IITV 

VMT 



y*3 

•gy 

Octave.         Seventh. 


Sixth. 


Fifth. 


Sixth 
becomes 


Seventh 
becomes 


-<5>- 

Octave    Augmented  Diminished 
becomes      becomes       oecomes 


Fourth. 


Third. 


Second.          Prime.   Diminished. Augmented. 


72.  From  the  above  let  us  notice  the  following :  — 
(a.)  To  learn  what  will  be  the  inversion  of  an  interval 
(that  is,  the  interval  which  will  result  by  inverting),  sub- 
tract the  number  of  the  interval  from  9,  and  the  result 
will  be  the  interval  produced  by  the  inversion.  For  ex- 
ample, what  would  the  interval  of  a  Sixth  become  by 
inversion?  Process  :  9  —  6=3;  therefore,  a  Sixth, 
when  inverted,  becomes  a  Third.  (See  p.  42,  Ad- 
dendum.) 

The    following  table     shows     the    fact   still     more 
clearly  : — 

From          9         9         99         9         9         9         9 
Substract    12345678 


Result        8 


HARMONY  SIMPLIFIED. 


35 


From  the  first  table  (Fig.  23)  we  notice  also  :  — 
73*   0^0  By  inversion  (  Major  intervals  become  Minor. 
By  inversion  (  Minor  intervals  become  Major. 

f  Augmented    intervals    become 
By  inversion          Diminished. 

By  inversion  1  Diminished     intervals    become 
Augmented. 

T,     .  .       f  Perfect    intervals    remain   Per- 

By  inversion  < 

(  feet  (and  therefore  Normal). 

This  peculiarity  of  the  Perfect  intervals  renders  it 
necessary  to  class  them  differently  from  the  Major,  though 
in  practical  Harmony  this  distinction  does  not  affect 
their  use.  A  further  difference  between  Major  and  Per- 
fect intervals  appears  in  §  76. 

Keyboard  and  Written  Exercises. 

74.  (a.)   Find  the  Perfect  intervals  in  Fig.  2  1  .    (There 
are  four.) 

(<5.)  From  the  note  D  form  a  series  similar  to  Fig. 
21,  and  invert  each  interval  as  shown  in  Fig.  23. 

(c.)  Write  examples  of  Diminished  and  Augmented 
intervals,  and  invert  them.  To  learn  what  Diminished 
and  Augmented  intervals  are  in  use,  the  pupil  may  refer 
to  the  Table  in  §  64. 

Consonant  and  Dissonant  Intervals. 

75.  In  the  preceding  paragraphs,  intervals  were  classed 
according  to  the  number  of  half-steps  contained.      They 
are  also  classed,  according  to  their  musical  effect,  as  :  —  • 

(a.)  Consonant,  meaning  those  intervals  upon 
which  it  is  agreeable  to  pause,  and  which  do  not  need 
to  be  followed  by  another  interval  to  produce  a  pleasant 
effect  ;  and 


HARMONY  SIMPLIFIED. 


(6.)  Dissonant,  or  those  which  are  not  satisfactory  to 
dwell  upon,  or  to  use  in  the  final  chord  of  any  composition. 

Consonances  are  further  divided  into  Perfect  and 
Imperfect  Consonances,  with  reference  to  the  degree  of 
concord,  as  follows  :  — 

All  Perfect  intervals,  viz., 
Perfect  Prime  (or  Unison), 
Perfect :  *    -}  Perfect  Octave, 

Consonances.  \  Perfect  Fourth, 

Perfect  Fifth. 

(  Major  Thirds  and    Sixths. 
Imperfect:  j  Minor  Thirds  and  Sixths. 

Seconds  and  Sevenths,  together  with  all 
augmented  and  diminished  intervals  ;  i.  e. , 
Dissonances.  -|  all  intervals  other  than  the  Perfect  inter- 
vals and  Major  and  Minor  Thirds  and 
Sixths. 

Exercises. 

(a.)  The  pupil  will  refer  to  all  the  previous  exercises 
and  illustrations  in  this  chapter,  particularly  to  the  Table 
in  §  64,  and  mark  each  interval  as  Perfect  or  Imperfect 
Consonance  or  Dissonance. 

(3.)  Both  at  the  keyboard  and  in  writing,  form  first 
all  the  consonant  intervals  and  then  the  Dissonant  inter- 
vals from  the  note  D. 

(c.)    Proceed  similarly  from  the  other  notes. 

76.  A  furthur  difference  between  Major  and  Perfect 
intervals  appears  at  this  place.  When  a  Major  interval 

*  The  distinction  between  perfect  and  imperfect  consonances  is  of  no 
importance  to  the  general  student,  who  will  recognize  an  interval  or  chord 
either  as  a  consonance  or  a  dissonance.  There  need  be  no  further  distinction 
at  present. 


HARMONY  SIMPLIFIED.  37 

is  decreased  by  a  semitone  (see  §  62),  it  becomes  a 
Minor  Interval,  but  its  classification  as  Consonant  or 
Dissonant  is  never  changed  by  this  reduction.  For  ex- 
ample, a  major  6th  being  consonant,  the  minor  6th  will 
be  consonant ;  or,  the  major  2nd  being  dissonant,  the 
minor  2nd  will  also  be  dissonant,  as  shown  in  the  above 
table ;  whereas,  if  a  Perfect  interval  be  decreased  by  a 
semitone,  it  at  once  loses  its  characteristic  of  being 
"Consonant"  and  becomes  a  "Dissonant"  interval. 


For  example,  f(g)    &   '  is  a  Perfect  Fifth.     If  we  lower 


the  upper  note  a  semitone,  the  result  is  L/rrV    b^?     >  which 

is  a  Diminished  Fifth  and  a  Dissonance.  Thus  we  see 
that  a  Major  interval  can  be  made  less  (Minor)  ivithout 
changing  its  classification  of  "Consonant";  while  a 
Perfect  interval  cannot  preserve  its  original  classification 
when  thus  altered.* 


Confusion  of  Terms. 

77.  There  is  much  confusion  in  the  terms  used  in 
connection  with  the  Theory  of  Music.  Carefully  notice 
to  what  each  term  refers.  A  few  examples  are  given 
below  of  the  various  meanings  of  certain  words  :  — 

Degree  may  refer  to  the  various  steps  of  the  Scale. 

Degree  may  also  refer  to  the  lines  and  spaces  of  the 
staff. 

Steps  may  refer  to  the  various  degrees  of  the  Scale. 


*  The  word  "  Perfect "  conveys  but  little  meaning,  as  these  intervals  are 
perfect  only  in  respect  to  their  quality  of  remaining  "  Normal "  when  inverted, 
while  Major  intervals  do  not.  A  more  descriptive  name  might  be  "  Sensitive '' 
Interval,  as  such  an  ir  terval  cannot  be  changed  in  any  manner  without  produc- 
Ing  a  dissonance. 


38  HARMONY  SIMPLIFIED. 

Steps  and  Half- Steps  also  to  the  distance  between 
tones. 

Tones  and  Semitones  may  refer  to  the  distance  be- 
tween tones. 

Tones  may  also  refer  to  sounds,  regardless  of  dis- 
tance from  other  sounds.* 

Interval  refers  to  distance  between  tones. 

Interval  sometimes  refers  to  the  steps  of  the  scale. 

The  names  of  the  Degrees  of  the  Scale  (  as  Fifth 
degree,  Third  degree,  etc.),  are  liable  to  be  confused  with 
the  Intervals  of  the  same  name :  therefore  be  careful  to 
say  whether  you  mean  Degree  or  Interval. 

Definitions. 

78.  Diatonic  Intervals.  The  word  Diatonic  refers  to 
the  scale ;  a  Diatonic  interval  would  be,  therefore,  an  in- 
terval formed  by  two  notes  of  the  scale  without  sharps  or 
flats  other  than  those  indicated  by  the  signature. 

Chromatic  Intervals.  The  word  Chromatic  in 
Music  refers  to  the  half-steps  lying  between  the  notes  of 
the  scale,  and  which  are  produced  by  the  use  of  acciden- 
tal sharps,  flats,  or  naturals,  to  change  the  diatonic 
tones.  A  Chromatic  interval,  then,  would  mean  one 
where  at  least  one  of  the  notes  has  an  accidental  sharp, 
flat,  or  natural  before  it. 

N.  B.  A  Half-step  can  be  either  Chromatic  or 
Diatonic;  e.  g.,  from  C  to  C$  is  a  Chromatic  half-step, 
because  only  one  note  (  C  )  is  concerned  in  the  interval. 
(  See  §  44.)  But  if  Q  is  called  Dfr,  the  half-steo  be- 
comes Diatonic,  because  two  notes  (  or  two  degrees  on 
the  staff")  are  concerned. 


•  The  words  Note  and  Tone  are  often  used  interchangeably,  though  a  tone 
k  properly  a  sound,  and  a  note  is  a  character  to  represent  a  sound  to  the  tye, 


HARMONY  SIMPLIFIED. 


39 


Enharmonic.  This  word  refers  to  the  notation 
only;*  when  the  same  tone  is  expressed  in  two  different 
ways,  there  is  said  to  be  an  Enharmonic  Change;  e.  g., 
Ab  when  changed  to  G#  is  said  to  be  enharmonically 
written,  because  the  name  has  been  changed  while  the 
tone  remains  the  same.  (  See  foot-note,  and  §  24.) 

This  chapter  should  always  be  studied  twice  (  repeated  very  care- 
fully )  before  proceeding,  as  it  is  impossible  to  understand  the  full 
meaning  of  the  first  part  before  the  last  part  has  been  studied. 

Synopsis. 

79.  Before  proceeding,  the  pupil  should  not  fail   to 
'write  a  synopsis  of  the  chapter  as  suggested  at  the  close 
of  Chapter  I,  and  endeavor  to  gain  an  orderly  view  of  the 
subject.     Failure  to  do  this  is  often  the  cause  of  very  con- 
fused ideas  in  regard  to  Harmony. 

Historical. 

80.  The  beginning  of  Music  was  Melody,  everything 
being  in  unison  and  without  accompaniment.     In  some 
MvSS.  of  the  loth  century,  examples  of  church-music  are 
found,  progressing  at  the  regular  interval  of  a  Fourth. 
The   meaning  of  this  has  been  disputed,  some  claiming 
that  it  was  intended  to  be  sung  in  unison  and  then  re- 
peated a  Fourth  higher,  while  others  think  the  two  parts 
were  to  be  sung  together,  the  effect  of  which  would  be 
disagreeable  to  modern  ears. 

At  about  this  time  a  "  Drone  Bass  "  was  sometimes 
used — i.  e.,  aBass  continuing  upon  one  note  regardless  of 
the  melody.  In  this  way  various  intervals,  such  as  Fourths, 
Fifths,  and  Sixths,  were  necessarily,  though  quite  acci- 
dentally, formed.  Soon  afterward  (nth  century  )  it  was 

*  Advanced  students  of  theory  may  know  that  Enharmonic  intervals  havti 
a  very  slight  difference  in  pitch  ;  e.  g.,  G$  has  a  few  vibrations  more  per  secon4 
than  Ak»  though  the  Piano  does  not  show  it. 


40  HARMON? 

discovered  that  two  complete  and  independent  melodies 
might  be  sung  together  and  produce  a  pleasant  effect. 
From  this  discovery  came  Counterpoint,  and  before  the 
close  of  the  I4th  century  music  was  written  in  four  parts, 
though  little  was  known  of  the  effects  of  harmony.  At 
this  period  the  controlling  principle  was  to  invent  several 
melodies  which  would  not  conflict  when  sung  together, 
rather  than  to  study  the  effect  of  the  combination  of  three 
or  four  tones  forming  a  chord.  Consequently,  at  this 
time,  till  the  close  of  the  14th  century,  the  harmonic 
effects  were  accidental  rather  than  studied. 

The  Perceptive  Faculties. 

(  Continued  from  page  24.) 

Intervals. 

81.  The  perception  of  intervals,  though  more  difficult  than  of  single 
tones,  need  not  cause  any  especial  trouble  if  properly  presented,  and 
if  the  first  steps  have  been  thorough.     It  is  probable  that  the  student 
will  advance  more  rapidly  in    Theory  than  in  the  development  of  the 
perceptions.     Do  not  try  to  make  the  two  keep  exact  pace,  though 
in  explaining  each  chapter,  the  ear  as  well  as  the  eye  and  the  under- 
standing should  be  actively  interested. 

Process. 

82.  ist  Step.    This  chapter  should  be  taught  as  a  direct  continua- 
tion of  the  lessons  on  the  degrees  of  the  scale,  not  as  a  new  subject. 
For  example,   taking  up   the    subject   at   (c),  §49,  after  singing  or 

playing    /r>      •     j     and   the  succession  has  been  named  Doh,  Ray, 

tZvl/.         _{_ 
O     -<5>-^ 

by  the  class  and  written  in  notes,  call  attention  to  the  fact  that  the  pro- 
gression has  been  explained  in  Chapter  II  as  an  interval  of  a  Second. 
(This  forms  a  Melodic  interval;  see  §  $4.)  In  a  similar  way,  the 
teacher  may  proceed  up  the  scale,  the  next  time  taking  the  notes  D 
and  E,  the  third  time  E  and  F,  etc.,  being  careful  that  the  pupils  do 
not  lose  sight  of  the  syllabic  names.  As  often  as  they  forget  or  miss 
them,  return  to  Doh,  and  let  them  sing  (or  recognize)  up  to  the  desired 
notes. 


HARMONY  SIMPLIFIED. 


41 


N.  B.  Being  a  dissonance,  the  two  notes  of  the  interval  of  the 
Second  should  not  be  sung  together,  unless  once  or  twice  merely  to 
show  their  dissonant  character. 


83.  2nd  Step.     Sing  or  play  the  notes  I  /k — ; — j — ,  requiring  the 

«J     «Sf-  6f~ 

syllabic  names  as  before,  and  allow  them  to  be  written.  Explain  that 
this  progression  forms  a  Third,  and  proceed  up  the  scale,  taking  the 
notes  D  and  F,  E  and  G,  as  shown  above,  requiring  first  the  syllabic 
names,  after  which  they  should  be  written. 

Next,  returning  to  C  and  E,  ailow  part  of  the  class  to  sing  the 
lower  note,  calling  it  Doh,  while  the  remainder  sing  E,  calling  it  Me. 
This  illustrates  the  Harmonic  interval,  as  singing  in  succession  repre- 
sented the  Melodic. 

Continue  up  the  scale  as  before,  but  now  allowing  both  notes  to 
be  sung  together  and  properly  written  to  express  the  harmonic 
interval. 

84.  yd  Step.     Treat  Fourths,  Fifths,  Sixths,  Sevenths,  and  Octaves 
(  not  exceeding  the  limit  of  the  voices  )  in  a  similar  manner,  first  Melod- 
ically,  and  then  Harmonically. 

Carefully  call  attention  to  the  musical  effect  of  the  different  inter- 
vals as  well  as  to  the  various  distances  apart. 

85.  4/A  Step.     Sing  or  play  successions  of  two  single  notes,  requiring 
first  the  syllabic  names  and  then  the  interval. 

86.  5//4  Step.     Play   various   intervals  (  harmonic),  first   striking 
the  notes  in  succession  ("spreading")  if  necessary,  requiring  both 
the   syllabic   names   and   name    of   the   interval.      Let  everything  be 
written    as   soon    as    the    pupil    recognizes   it,   to  gain  the  habit  of 
expressing  his  impressions.      (Begin  this  step  [§86]  with  Octaves 
and  Fifths.) 

87.  6th  Step.     Striking  a  Major  Third,  change.it  to  Minor  by  low- 
ering the  upper  note,  calling  attention  to  the  different  musical  effect 
and  the  means  of  producing  it ;  explaining  at  the  same  time  that  some 
of  the  Thirds  in  the  scale  are  Minor  without  any  change,  for  example, 
from  Ray  to  Fah,  Me  to  Soh,  etc. 

88.  jth  step.     Display  Major  and  Minor  Sixths  in  a  similar  manner. 
Introduce  Diminished  and  Augmented  intervals  very  cautiously,  on 
account  of  their  difficulty. 


42  HARMONY  SIMPLIFIED. 

89.  In  general.  Arrange  the  exercises  carefully  in  point  of  pro- 
gressive difficulty.  Do  not  let  the  pupil  get  confused  in  regard  to 
the  syllabic  names.  He  must  ha"ve  a  firm  hold  of  the  Tonality.  Be 
patient. 

The  pupil  may  now  take  two-part  songs  ( or  the  soprano  and  alto 
of  hymns  and  choruses  ),  and  try  to  think  how  they  would  sound 
afterward  comparing  with  the  effect  when  played  or  sung. 

Exercises  in  Rhythm  should  be  continued. 

(Addendum  to  §  72.) 

Complementary  Intervals. 

Any  two  intervals  which, when  added  together,form  an  octave,  are 
called  Complementary  intervals,  since  each  completes,  or  complements 
the  other  in  the  formation  of  the  octave.  This  is  simply  another  state- 
ment of  Inversion,  for  any  interval  and  its  inversion  form  Comple- 
mentary intervals.  Illustration : —  A  Sixth  and  a  Third  are  Comple- 
mentary, or  the  Sixth  is  said  to  be  Complementary  to  the  Third,  and 
vice -versa.  Similarly,  Fourths  and  Fifths,  or  Seconds  and  Sevenths, 
are  Complementary. 


HARMONY  SIMPLIFIED.  43 

PART  II. 


CHAPTER  III. 

TRIADS. 

The  Foundation  of  the  Harmonic  System. 

NOTE.  §  90  is  not  to  be  studied.  It  is  designed  more  especially 
for  the  teacher  and  for  those  inquiring  minds  who  would  know  some- 
thing of  the  scientific  basis  of  chord-formation,  and  observe  the  won- 
derful symmetry  and  simplicity  of  Nature's  laws. 

Advanced  Course. 

Harmonics. 

90.  Science  has  demonstrated  that  a  musical  tone  is  not  one  simple 
sound,  but  is  made  up  of  the  combined  sounds  of  many  different  tones, 
softly  sounding  with  the  principal  or  Primary  tone.  It  has  also  been 
proved  that  these  secondary  tones  bear  a  certain  relation  to  the  prin- 
cipal or  Primary  tone,  and  though  they  sound  but  faintly  (being 
inaudible  to  untrained  ears  ),  can  be  distinctly  recognized  by  those 
who  are  trained  in  this  direction.  These  secondary  or  accompanying 
tones  are  called  Overtones  or  Harmonics. 

When  a  long  string,  tightly  drawn,  is  put  into  vibration,  it  vibrates 
in  its  full  length  alone  only  an  instant  ;  after  a  short  time  it  vibrates 
also  in  sections  (  without  interfering  with  the  full-length  vibrations  ) 
producing  higher  tones  simultaneously  with  the  principal  or  funda- 

mental tone.     For  illustration,  if  a  string  producing  the  tone  KJ 


__ 

is  put  into  vibration,  this  tone  will  be  very  distinct,  but  the  presence 
of  the  following  tones,  sounding  very  faintly,  can  be  proved. 


Flg.24.p2-    --&-{- 


*  These  harmonics  are  not  exactly  true  to  pitch. 


44 


HARMONY  SIMPLIFIED. 


This  series  is  called  the  Harmonic  Chord,  or  Nature's  Chord 
Those  who  are  already  familiar  with  chords  will  observe,  that  the 
first  six  notes  sounded  together  are  simply  an  ordinary  chord.  If  the 
next  note,  Bfr,  is  added,  a  Chord  of  the  7th  is  formed.  If  to  the  last 
chord  the  ninth  note  of  the  series  is  added  ( the  eighth  note,  C,  is 
merely  a  duplicate  of  the  lower  octaves),  a  chord  of  the  Ninth  is 
formed.  In  these  three  chords,  or  rather  in  this  one  Harmonic  Chord, 
is  the  basis  of  the  Harmonic  system,  from  which  the  various  chord- 
formations  can  be  logically  developed.  The  above  is  designed  to  show 
four  points,  viz: — 

(  a.)  That  a  musical  tone  is  made  up  of  many  tones  sounding 
together  as  above  stated.* 

( 6.)  That  a  chord,  as  commonly  understood,  is  an  imitation,  at 
the  hands  of  Man,  of  the  great  chord  of  Nature,  or  at  least  it  has  been 
made  to  correspond  very  closely  with  it. 

NOTE.  Young  students  are  liable  to  be  troubled  by  the  fact  that 
some  of  the  remoter  harmonics  are  strongly  dissonant  with  the  funda- 
mental tone  and  triad.  But  this  need  not  disturb  them,  as  the 
harmonics  are  more  indistinct  as  they  are  more  remote  from  the 
Fundamental  tone,  and  the  finest  ear  cannot  detect  more  than  six  or 
seven.  Therefore,  the  upper  ones  are  too  weak  to  have  much  effect 
upon  a  tone,  though  Science  conclusively  proves  their  presence. 

( c.)  That  chords  are  produced  by  a  process  of  adding  to,  or 
building  upon,  a  note  called  the  Fundamental,  or  Root.  The  Chord  of 
the  7th  was  produced  by  adding  one  note  to  the  chord  already  formed  ; 
and  the  Chord  of  the  gth,  by  adding  still  one  more. 

(d.)  Conversely,  that  the  chord  built  upon  a  Root  is  considered 
as  derived  from  that  Root. 

Regular  Course. 

Triads. 

91 .  When  any  note  is  taken,  together  with  the  intervals 
of  a  Third  and  a  Fifth  above  it,  a  Triad  is  formed.  A 
Triad,  then,  is  a  chord  of  three  notes :  a  Fundamental 


*  There  is  a  strong  analogy  between  a  single  tone  and  a  ray  of  light.  When 
thrown  through  a  prism,  light  is  seen  to  be  a  compound  of  various  colors,  the 
prism  serving  to  separate  the  ray  into  its  constituent  parts.  Similarly,  a  tone 
can  be  shown  by  the  laws  of  sympathetic  vibration  to  consist  of  the  Primary 
tone  and  Overtones,  as  shown  in  §  90. 


HARMONY  SIMPLIFIED.  45 


or  Root,  together  with  its  Third 

and  Fifth,  counting  upward  ;  e.  g.,  — ^ — 

As  shown  above,  the  whole  Harmonic  System  may 
be  said  to  rest  upon  this  simple  Triad.  A  distinguished 
musician  has  declared,  "There  is  but  one  chord  in  the 
world,  the  Common  Triad.  All  others  are  merely  addi- 
tions to  this." 

Exercises. 

(  a.)  Write  the  scale  of  C,  and  upon  each  note,  used 
as  a  Fundamental,  construct  a  triad,  without  considering 
whether  the  intervals  are  Major  or  Minor  (see  Fig.  25). 


Fig.  25. 


, »- 


(  3.)  Write  similarly  the  scale  of  G,  F,  D,  B,  etc., 
not  regarding  sharps  or  flats  except  to  place  them  in  the 
signature,  and  construct  a  triad  upon  each  note,  as  above. 

(c.)  Repeat  the  above  exercises  at  the  keyboard, 
and,  in  addition,  take  each  of  the  remaining  major  keys. 

Marking  the  Triads. 

92.  In  §  2  it  was  shown  how  each  degree  of  the  scale 
is  numbered  from  the  lowest  to  the  highest.  The  Triads 
are  described  in  a  similar  manner,  by  indicating  upon 
which  degree  of  the  scale  they  are  founded ;  for  exam- 
ple, "Triad  on  the  3d  degree, "  "  Triad  on  the  6th 
degree,"  etc.  For  this  purpose  Roman  Numerals  are  em- 
ployed, being  written  under  the  staff  as  shown  in  Fig.  26. 


Fig.  26. 


I  II         in        IV        V        vi        vn°     I 

Exercises. 
Mark  the  Triads  formed  in  the  exercises  in  §  91. 


46  HARMONY  SIMPLIFIED, 

Specific  Names  of  Triads. 

93.  Triads  are  divided  into  four  kinds,  Major,  Minor. 
Diminished,    and    Augmented.      These    varieties    corre- 
spond closely  with  the  intervals  of  the  same  names,  for 
they  are   named,   according  to   the  intervals  of  'which 
they  are  composed*  as  follows :  — 

A  Major  triad  has  a  Major  3rd  and  Perfect  5th. 

A  Minor  triad  has  a  Minor  3rd  and  Perfect  5th. 

A  Diminished  triad  has  a  Minor  3rd  and  Dimin.  5th. 

An  Augmented  triad  has  a  Major  3rd  and  Aug- 
mented 5th. 

These  four  kinds  of  triads  are  indicated,  in  marking 
the  triads,  as  follows  : — 

Major,  by  a  large  Roman  numeral,  for  example  :  I. 

Minor,  by  a  small  Roman  numeral,  for  example :  n. 

Diminished,  by  a  small  Roman  numeral  with  the 
sign  °  affixed  :  vn°. 

Augmented,  by  a  large  Roman  numeral  with  the 
sign'  affixed :  III'. 

Exercises. 

(  a.)  Write  the  Harmonic  Minor  scale  of  A,  and  form 
triads  upon  the  various  steps,  as  in  §  91.  Next,  describe 
each  triad  (  Major,  Minor,  Diminished,  or  Augmented), 
and  mark  as  above  indicated. 

(3.)      Repeat  the  process  in  E,  D  and  B  minor. 

(c.)  Repeat  the  above  at  the  keyboard,  adding 
other  Minor  keys. 

Principal  and  Secondary  Triads. 

94.  The  triads  upon  the  Tonic,    Dominant  and   Sub- 
dominant  ( see  §  34  )  are  called  the  Principal  or  Primary 
Triads,  for  the  following  reasons  :  — 

(a.)  They  are  most  frequently  used. 

(3.)  They  embrace  every  note  of  the  scale. 


HARMONY  SIMPLIFIED.  47 

(c.)  They  are  sufficient  to  determine,  beyond  doubt, 
{he  key. 

The  Triads  upon  the  remaining  degrees  are  called 
Secondary  Triads. 

Exercises. 

Returning  to  the  exercises  in  §§  91,  92,  93,  the  pupil 
will  describe  each  Triad,  indicating  the  Secondary- 
Triads  by  the  proper  Roman  numeral,  and  the  others  by 
the  first  letter  of  their  names ;  thus,  T,  ( Tonic)  ;  D, 
(  Dominant  )  ;  and  S.  D,  (Subdominant). 

Doubling. 

95.  In  a  Triad  there  are  but  three  different  notes. 
Therefore,  if  we  write  music  in  four  parts,  one  of  the 
three  notes  must  be  doubled,  i.  e.,  must  appear  in  two 
parts.  The  Fundamental  is  the  best  note  for  doub- 
ling, and  the  Third  che  poorest.  (See  §  162.)  The 
four-part  chord  resulting  from  the  doubling  of  one  note 
of  the  triad  is  called  a  Common  Chord  ;  e.  g., 


or:< 


Position. 

96.  The  three  notes  composing  the  Triad  do  not  need 
to  be  always  in  the  same  order,  with  the  Fundamental 
lowest  and  the  Fifth  at  the  top.  The  Fundamental  of 
the  Third  may  also  occupy  the  highest  place,  and  the  term 
Position  is  used  to  denote  which  note  is  highest,  as 
follows : — 

(  a.)  When  the  Fundamental  or  its  octave  is  highest 
( in  the  Soprano  )  the  chord  is  said  to  be  in  the  Position 
of  the  Octave. 


y                         E___s             I         <= 

X                sy                      \               <y                      \               & 

¥\\             <^                  \             'n'                1 

^\)        g           iznms.           * 

Ci*                                        1                                        1 

iJJ                                                                IT                                  1 

S                            &                                  \                       &                                  \                       C, 

1                                                               1 

^8  HARMONY  SIMPLIFIED. 

(  £.)  When  the  Third  is  highest,  the  Chord  is  in  the 
Position  of  the  Third. 

(c.)  When  the  Fifth  is  highest,  the  chord  is  in  the 
Position  of  the  Fifth. 


Fig.  27.< 


Position  of  the  Octave.   Position  of  the  3d.     Position  of  the  5th. 

Keyboard  and  Written  Exercises. 
(  #.)    Form  the  triad  upon  each  of  the  remaining 
degrees  of  the  key  of  C,  showing  each  triad  in  its  three 
positions,  as  illustrated  in  Fig.  27,  which  gives  the  triad 
upon  the  first  degree.     Use  two  staves  in  writing. 

(b.)  Form  Major  triads  of  A,  E,  F,  At?  and  Bt>  in 
the  three  positions,  using  the  proper  (key-)  signatures 
in  each  case. 

Four-part  writing;  Connection  of  Triads. 
97.  Each  chord  of  four  notes  is  considered  as  written 
for  a  quartet  of  voices,  Bass,  Tenor,  Alto  and  Soprano. 
The  Soprano  and  Bass  are  called  the  Outer  or  Extreme 
parts :  the  Alto  and  Tenor  are  called  the  Inner  parts. 
In  four-part  writing  the  effect  should  be  considered  from 
two  points  of  view  : — 

(  a.)  The  Melodic  effect  of  each  part  (as  it  would 
sound  if  sung  alone). 

(  6.)  The  Harmonic  effect  of  the  four  parts  sounding 
together,  and  the  connection  between  the  successive 
chords. 

Before  proceeding  to  practical  exercises  in  connect- 
ing chords  and  leading  the  parts,  the  pupil  should  learn 
something  of  the  difficulties  in  the  way  of  making  a  good 
effect,  as  follows : — 


HARMONY  SIMPLIFIED.  49 

Consecutive  Fifths. 
98.     If  we   play   a   series    of    Thirds,  for    example, 


IJ  gj_d  etc.,  the  effect  is  not'  unpleasant.     If 


we  add  a  Fifth,  changing  each  Third  to    a    triad,   thus : 
etc.,  we  find  the  effect  harsh  and  un- 


pleasant.    This    disagreeable    effect  was   evidently    not 
produced  by  the  Thirds  sounding  in  succession,  for  the 

,     Q        ,       |       |      4—1., 
following:      /f        \—&    a ^ ^^  etc.,    is,  if  possible, 

~ — 


still  worse.     Therefore,  we   may  conclude  that  the  bad 
effect  is  produced  by  the  succession  of  Fifths.* 

Consequently,   Consecutive  Fifths  are  not  allowed. 

Consecutive  Octaves. 

99.  Again,  if  in  a  four-part  chorus  two  voices  sing  the 
same  notes,   either  in   unison  or  an  octave  apart,  there 
would  be  in  reality  but  three  different  parts,  which  would 
weaken  the  harmony.     Therefore,   Consecutive  Octaves 
{and  Unisons)  are  not  allowed. 

100.  In  order  to  learn  how  to  avoid  Consecutive  Fifths 
and  Octaves,  the  pupil  should  realize  that  in  the  progres- 
sion of  the  parts,  three  different  movements  are  possible  : — 

(  a.)  Parallel  Motion,  in  which  two  parts  move  in  the 
same  direction ;  see  (  a ),  Fig.  28. 

( b.~)  Oblique  Motion,  in  which  one  part  remains 
stationary,  while  the  other  moves;  see  (  b  ),  Fig.  28. 

(c.)  Contrary  Motion,  in  which  the  parts  move  in 
opposite  directions:  see  (  c),  Fig.  28. 


*  The  harshness  of  consecutive  sths  is  caused  by  the  suggestion  of  two 
different  keys  in  succession  without  proper  (modulatory)  connection.  If  the 
second  interval  is  a  diminished  fifth,  a  new  key  is  not  so  strongly  suggested: 
hence  this  exception  is  allowed. 


50  HARMONY  SIMPLIFIED. 


Fig.  28. 


In  four-part  writing,  two  or  even  three  different 
kinds  of  motion  can  occur  simultaneously  between  the 
different  parts.  Parallel  motion  between  three  parts  is 
permitted,  if  no  Consecutive  Fifths  or  Octaves  result  from 
it.  Parallel  motion  between  all  four  parts  is  not  good, 
and  it  is  difficult  to  avoid  the  forbidden  consecutives  if  the 
parts  all  move  in  the  same  direction. 

To  Avoid  Consecutive  Fifths  and  Octaves. 
Let  one  or  two  parts  progress  in  contrary  motion  to  the  others. 
This  rule  will  cover  all  cases. 

Open  and  Close  Harmony. 

101.  When  the  Soprano,  Alto  and  Tenor  all  lie 
within  the  compass  of  an  octave,  the  parts  are  said  to  be 
written  in  Close  Harmony.  If  they  exceed  the  compass 
of  an  octave,  they  are  in  Open  Harmonv 

Close  Harmony.    Open  Harmony. 


Fig.  29.< 


Close    Harmony  should  be    used   in  the  following 
chapters  unless  otherwise  indicated. 

To  Connect  Two  Triads. 

NOTE.    The  following  is  of  especial  importance,  and  should  be 
thoroughly  mastered  before  proceeding. 

1 02.  Under  this  head  two  cases  are  to  be  considered :— 


HARMONY  SIMPLIFIED.  51 

(  a.)  When  the  two  given  chords  have  one  or  more 
nates  in  common. 

(  b.)  Where  there  is  no  common  tone  to  serve  as  a 
connecting-link. 

When  the  Chords  have  a  Note  in  Common. 

Let  us  take  C  —  E  —  G  and  A  —  C  —  E,  for  example, 
to  connect.  Having  two  notes  in  common,  it  is  evident 
that  there  is  a  close  connection  between  them,  and  it  is 
only  necessary  to  make  this  connection  apparent  to  the 
ear.  If  we  play  the  two  chords  thus  : 


there  is  to  the  ear  no  connection   whatever.     But  when 

r     Q  — 

played  thus :     /^  „    •  the  connection  is  very  ap- 


parent.  This  is  because  the  notes  common  to  both 
chords  are  retained  in  the  same  parts.  That  is,  the 
Tenor  and  Alto,  which  have  the  notes  C  and  E  in  the 
first  chord,  retain  them  in  the  second.  Therefore,  notes 
common  to  both  chords  are  to  be  retained  in  the  same 
•parts. 

It  will  be  seen,  that  to  follow  this  all-important 
principle,  the  "  position"  of  the  chords  must  be  adapted 
to  the  necessities  of  the  situation,  sometimes  one  note 
being  highest  and  sometimes  another. 

The  Process. 

103.  The  following  is  given  to  illustrate  the  mental 
process  by  which  the  beginner  should  solve  every  prob- 
lem. Having  written  the  first  chord  in  notes : — 

ist  step.     What  are  the  notes  of  the  second  chord  ?* 


•  This  question,  though  unnecessary  here,  is  of  importance  when  the  pupil 
begins  to  work  exercises  from  a  given  Bass,  as  in  §  in. 


5  2  HARMONY  SIMPLIFIED. 

(  N.  B.  If  the  pupil  has  trouble  in  keeping  the  notes  of  the  sec- 
ond chord  in  mind  during  the  following  steps,  he  may  write  them 
on  a  separate  slip  of  paper.) 

2nd  step.  Is  any  note  common  to  both  chords  ? 
What  note  is  it? 

3rd  step.  In  which  part  (Soprano,  Alto,  etc.)  of 
the  first  chord  is  this  "common"  note  found?  Ans. 
In  the —  (Here  mention  whether  it  is  Soprano,  Alto^ 
Tenor,  or  Bass  ) ,  therefore  it  must  appear  in  the  same 
part  in  the  second  chord. 

4th  step.  Write  it,  and  connect  with  the  same 
note  in  the  first  chord  by  a  tie.  (Do  not  write  any 
other  notes  yet.) 

$th  step.  Name  the  remaining  notes  of  the  second 
chord. 

6th  step.  Which  "position"  of  the  second  chord 
will  enable  the  remaining  notes  of  the  first  chord  to  pro- 
gress in  the  smoothest  manner  to  the  remaining  notes  of 
the  second  chord? 

Illustration. 
104.  To   connect   the    triads    C-E-G,   written    thus: 


tflT    -<y  ~"  anc^  G-B-D. —  It  is  apparent  that    G  is   the 

"common"  note  or  connecting-link.  Therefore,  as  G 
is  in  the  Soprano  in  the  first  chord,  it  must  be  in  the 
Soprano  in  the  second;  according  to  §  103,  4th  step,  we 

have  :  [  ^      ^—^    -.     It  is  now  apparent  that  the  remain- 


ing notes  of  the  second  chord,  B  and  D,  must  lie  be- 
low   G    (as    the  Soprano  is   always  the  highest  part), 


thus :  r/T\     .;tfr"r>v?  As  this  makes  a  smooth  leading 


HARMONY  SIMPLIFIED.  53 

of  the  Alto    and   Tenor  (  no   wide   skips*)  the  effect  is 


If  the  first  chord  is  in  this  position  : 


the  connecting  note,  being  G,  is  in  the  Alto  in  the  first 
chord,  and  must  appear  in  that  part  in  the  second 
chord.  Now  it  is  plain  that  we  must  so  arrange  the 
remaining  notes  of  the  second  chord,  B  and  D,  that 
the  Soprano  and  Tenor  of  the  first  chord  ivill  each  have 
a  note  to  which  it  may  progress  ;  therefore,  we  cannot 
place  both  B  and  D  below  G,  as  was  the  case  before,  but 
one  should  be  above  and  one  below,  and  the  choice  ot 
position  must  depend  upon  the  possibility  of  making  a 
smooth  progression.  Let  us  try  with  D  above  and  B 

below,  giving  :  p^    tv,*—^5*    ,  and  compare  it  with  the 

~&~ 

effect  when  we  place  the  B  above  and  D  below,  thus  : 

__     It  will  be  seen  that  although  the  former 

— 


^ 


will   answer,  the   latter  gives  the   better  effect,   because 
there  are  no  skips.     Again,  taking  the  first  chord  in  this 

position  :     ~Y^    ^  ~?  we  find  the  connecting  note  in 


the  lowest  part ;   therefore,  both  the  remaining  notes  of 
the  second  chord^must  be  written  above  the  connecting 

note,  giving : 

Keyboard  and  Written  Exercises. 
105.  (a.)  Connect  the  triad  of  C  with  that  of  F  Major, 


*  In  the  early  exercises  the  parts  should  not  make  very  wide  skips  from 
note  to  note,  but  should  progress  by  the  smaller  intervals  ( ands  and  3rds)  wher- 
ever possible.  In  composition,  where  the  parts  progress  by  the  smaller  inter- 
vals, the  effect  is  restful  and  tranquil.  Where  they  progress  by  the  larger 
intervals,  such  as  4ths,  5th,  6ths,  and  Sves,  the  effect  is  bolder  and  more 
aggressive. 


54 


HARMONY  SIMPLIFIED. 


taking   successively  the   various   positions   of    the   first 
chord,  as  illustrated  above.     Use  one  staff  in  writing. 

(3.)  Connect    (  in  three  positions  )    the  triad  of  C 
maj.  with  that  of  E  min. ;  with  A  min. 

Connect  (  in  three  positions  )  the  triad  of  D  min. 
with  that  of  F  maj. ;  with  A  min. ;  and  with  G  maj. 

Connect  ( in  three  positions )  the  triad  of  E  min. 
with  that  of  C  maj. ;  with  G  maj. 

Connect  ( in  three  positions  )  the  triad  of  E  min. 
with  that  of  A  min. 

Connect  (  in  three  positions  )  the  triad  of  F  with 
triads  upon  C,  A,  and  D  (  all  in  the  key  of  C  ) . 

Connect  (  in  three  positions  )  the  triad  of  G  with 
triads  upon  C,  E,  and  D 

Connect  ( in  three  positions  )  the  triad  of  A  with 
triads  upon  C,  D,  F,  and  E. 

Connect  ( in  three  positions )  the  triad  of  B  with 
triads  upon  E,  D,  and  F. 

Note  that  all  the  above  are  in  the  key  of  C  Major. 

(c)  Transpose  (  b  )  into  other  keys,  and  rej^eat. 
(  This  transposition  will  not  be  difficult,  if  we  remember 
that  to  transpose  a  note  or  a  chord  it  is  given  the  samo 
relative  place  in  the  new  key  that  it  occupied  before  being 
transposed.  E.  g.,  if  a  triad  is  on  the  second  degree  in  the 
key  of  C,  when  transposed  it  must  be  placed  upon  the 
same  degree  of  the  new  key :  if  on  the  fifth  degree  in  the 
original  key,  it  must  be  placed  upon  the  same  degree  in. 
the  new  key.  Likewise  the  ' '  position "  and  inversion 
of  a  chord  must  correspond  when  transposed.  If  we 
substitute  the  Roman  Numerals  (  as  shown  in  §  92  )  for 
the  letters  C^  D,  E,  etc.,  in  exercise  (  b  ),  it  will  be  easy 
to  find  the  notes  corresponding  to  these  numerals  in  any 
desired  key. 

(  d.)  Write  (  b  )  in  four  parts,  as  illustrated  in  Fig. 


HARMONY  SIMPLIFIED. 


55 


-X- 

1  —  J5  1  —  g  »  1 

$= 

3* 

.x« 

^       1                     ^       1                     ^         1 

•j. 

17 

3!  1—"  1—  ~  ' 

30;  the  root  of  each  chord  being  written  in  the  Bass, 
which  will  remain  the  same  for  all  positions. 


Fig.  S0.< 


To  connect  two  Triads  when  there  is  no 
Common  Note. 

106.  Although  two  given  chords  belonging  to  the  same 
key  may  not  have  a  visible  connection  by  means  of  a 
common  note,  there  is  a  certain  relationship  through  their 
being  members  of  the  same  key,  (  see  the  Author's  "How 
to  Modulate,"  §  3,)  and  with  a  careful   leading  of  the 
parts  they  may  be  used  in  succession. 

Especial  attention  must  be  given  to  avoid  consecu- 
tive Fifths  and  Octaves,  remembering  that  Contrary 
Motion  is  the  means  of  so  doing.  It  should  be  noticed 
that  some  Positions  are  much  better  than  others  for  a  given 
connection,  and  that  some  Positions  cannot  be  used  at  all. 
The  smoothest  connection  is  usually  where  the  three 
upper  parts  move  in  a  direction  contrary  to  the  Bassr. 

The  Process. 

107.  The  mental  process  of  finding  the  correct  leading 
of  the  parts  is  somewhat  as  follows : 

Example  for  illustration.  Connect  the  triad  of 
C,  in  the  position  of  the  3rd,  with  the  triad  of  D.  Ex- 
pressed in  notes,  thus : 


56  HARMONY  SIMPLIFIED. 

(1st  step.)  What  are  the  notes  of  the  Second 
chord?  Ans.,  D  F  A. 

(2nd  step.)  In  which  direction  does  the  Bass  move 
in  the  example?  Ans.,  Upward;  therefore  it  would  be 
well  to  have  the  three  upper  parts  (or  as  many  of  them  as 
possible)  move  downward  (  to  move  contrary  to  the  Bass) . 

(3rd  step.)  Which  position  of  the  second  chord 
allows  the  proper  progression  of  the  parts,  without  Con- 
secutive Fifths  and  Octaves? 

( Or,  3rd  step.)  Write  the  notes  of  the  second  chord, 
so  that  each  part  shall  progress  in  the  desired  direction, 
avoiding  Consecutive  Fifths  and  Octaves. 


(4th  step.)  Would  any  other  position  give  a  better 
leading  of  the  parts,  by  avoiding  large  skips  or  otherwise 
producing  a  better  general  effect?* 

N.  B.  All  of  the  upper  parts  are  not  obliged  to 
move  contrary  to  the  Bass.  Sometimes  it  is  better  to 
have  only  one  part  progressing  contrary  to  the  Bass. 

Fig.  31  illustrates  the  connection  of  the  triad  of  C 
(in  its  three  positions  )  with  that  of  D. 

_(«•)  <*•)  ('•)_ 


Fig.  31. 


*  There  are  other  influences  affecting:  the  leading  of  the  parts,  which  are, 
however,  as  yet  too  advanced  for  the  pupil.  After  having  studied  as  far  as  §170. 
the  pupil  should  review  this  section. 


HARMONY  SIMPLIFIED. 


57 


108.  At  (a)  it  is  necessary  to  double  the  Third  to 
avoid  Consecutive  Fifths  with   the   Bass,   which  would 
arise  if  the  Alto  should  progress  to  A.     Notice  also  that 
the  Tenor  should  not  progress  downward  to  D  at  this 
place,    as  bad  hidden  Fifths  with   the  Soprano  would 
result.      (See  §  134.) 

Exercises. 

109.  Copy  the  following,  and  fill  up  the  vacant  parts, 
aorjlying  the  "  mental  Process  "  to  each  of  the  ten  sepa- 
rate examples. 


Fig.  32.. 


Key  of  C :    n       in      in     IV     IV     V       V      vi      vi 


9i= 


I          ii      in          II       in       IV        V      in      IV 

The  above  examples  do  not  sound  well  unless  used 
in  connection  with  other  progressions,  when  they  lose 
much  of  their  harshness.  The  teacher  should  give  exam- 
ples in  other  keys,  and  as  soon  as  the  class  can  "  figure  " 
inversions  (see  §§  125-132),  this  section  should  be  again 
taken  up,  using  chords  in  their  inversions. 


Exercises. 
( a. )     In  the  key  of  G,  connect  the  triad  upon  each 


eg  HARMONY  SIMPLIFIED. 

degree  with  the  one  upon  the  degree  next  above,  trying 
the  different  positions  to  make  the  best  effect  possible. 

(  £.)     Repeat  in  the  keys  of  Bb,  A,  and  F. 

(c.)      Repeat  the  above  at  the  keyboard,  adding  all 
other  Major  keys. 

Review  of  the  Connection  of  Triads, 
no.     (  a.  )     Avoid  Consecutive  Fifths  and  Octaves. 

(  £.)   Contrary  motion  is  the  means  of  avoiding  them. 

(c.)  If  there  is  a  connecting  note,  keep  it  in  the 
same  part  in  both  chords. 

(  d.)  If  there  is  no  note  in  common,  adopt  contrary 
motion  and  avoid  wide  skips,  especially  guarding  against 
consecutive  Fifths  and  Octaves. 

(  e.)  In  doubling  notes,  the  Fundamental  is  the  best 
note,  the  Third  the  poorest.  The  Leading-note  should 
be  doubled  only  under  exceptional  circumstances :  though 
doubling  any  part  is  better  than  open  consecutives. 

(_/".)  Avoid  wide  skips.  Let  each  part  be  melo- 
dious. 

(,£".)  Avoid  progressions  of  Augmented  intervals, 
as  they  are  not  melodious. 

Part-writing. 

in.  Having  learned  to  connect  two  given  triads,  the 
pupil  should  proceed  to  put  his  knowledge  into  practical 
use  by  writing  exercises  on  given  Basses.  In  these  exer- 
cises is  nothing  new ;  each  exercise  may  be  considered 
as  a  little  series  of  examples  illustrated  in  §  §  102  to  no. 

N.  B.  A  figure  over  \hejirst  Bass  note  ot  an  exer- 
cise, indicates  whether  the  Third,  Fifth  or  Octave  of  the 
Bass  note  is  to  appear  in  the  Soprano. 

Should  the  pupil  need  further  guidance,  the  follow- 
ing •«  mental  process,"  illustrating  Fig.  33,  will  help. 


HARMONY  SIMPLIFIED. 


59 


33. 


m 


112.  Process:  The  Figure  8  over  the  first  note  indi- 
cates, that  we  are  to  begin  with  the  octave  (or  double 
octave  )  of  the  Root  as  the  highest  note,  giving  the 

chord  in  this  position  : 


The  first  problem  then  is,  to  connect  this  chord  with 
the  chord  founded  on  F,  as  indicated  by  the  second  Bass 
note  in  Fig.  33.  Now  let  the  pupil  go  through  the 
process  shown  in  §103,  giving  as  a  result: 


I 


i 


The  next  problem  is  to  connect  the  chord  last  found 
with  the  chord  founded  on  C,  as  indicated  by  the  third 
note  in  the  given  bass.  Following  th?  same  process 
brings  one  more  chord.  Continuing  in  the  same  way 
gives  the  completed  example  : 


Fig.  34.< 


IV 


113.  In  the  first  exercises  the  Soprano  part  is  given  a« 
well  as  the  Bass,  leaving  the  pupil  to  find  the  names  of 
the  remaining  notes  in  each  chord  and  to  place  thena 
80  that  they  will  progress  as  smoothly  as  possible. 


6o 


SIMPLIFIED. 


The  parts  should  not  cross ;  for  example,  the  Altr 
should  not  go  higher  than  the  Soprano  or  lower  thar 
the  Tenor.  Write  the  exercises  in  close  harmony. 

114.  The  various  parts  should  not  exceed  the  compass 
of  a   good  voice  of  corresponding  pitch,    as  shown  in 

Fig  35- 

Soprano. 


Alto. 


Bass. 


The  pupil  should  always  mark  the  Roman  numerals 
in  the  exercises,  as  shown  in  Fig.  34.  Always  write 
them  before  beginning  to  form  the  chords. 


1  15*                                    Exercises. 
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HARMONY  SIMPLIFIED. 


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1 1 6.  In  the  following  exercises  the  pupil  will  write 
the  Soprano  as  well  as  the  other  parts.  Where  the 
figure  3  is  found  over  the  first  Bass  note  in  an  exercise,  it 
indicates  that  the  first  chord  should  appear  in  the  posi- 
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the  5th  is  desired.  Where  no  figure  is  given,  the  posi- 
tion of  the  octave  is  to  be  written.  This  applies  to  the 
first  chord  only  of  each  exercise. 
1.  Jadassohn.  2.  Richter. 


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HARMONY  SIMPLIFIED. 
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Exercises. 

117.  The  pupil  is  recommended  to  repeat  the  exer- 
cises in  this  chapter,  starting  with  the  Soprano  in  a  db 
ferent  position,  in  order  to  realize  the  different  treatment, 
required  by  the  changed  circumstances.  It  will  be  found 
that  some  of  the  exercises  cannot  be  worked  out  so 
smoothly  in  one  position  as  in  another ;  consequently,  by 


HARMONY  SIMPLIFIED.  63 

this  practice,  the  judgment  will  be  sharpened  to  discern 
the  choice  in  progressions. 

118.  In  cases  where  this  book  is  used  as  a  preparation 
for  the  study  of  Analysis,  or  for  Piano-students  who  are 
unwilling  to  study  Harmony  ( part-writing )  but  who 
desire  to  thoroughly  understand  the  construction  of  the 
chords,  the  above  exercises  may  be  omitted.  In  their 
place  the  pupil  may  take  Sonatinas,  Sonatas,  etc., 
mark  the  key,  indicate  upon  which  degree  of  the  scale 
each  triad  is  found,  and  its  classification  (  Major,  Minor, 
etc.).  He  should  be  taught,  that  in  considering  the 
harmonic  structure  of  a  composition,  a  broken  chord  is 
marked  the  same  as  one  which  is  not  broken.  For  ex- 
ample, (a  ),  (  b  ),  and  (  c  )  of  Fig.  36  are  all  considered 
to  be  the  chord  on  C,  and  are  marked  accordingly. 

(c.) 

4^ 

Fig.  36.   ; 


C:    I      I~7   .    ....          I 

This   practice   is   also  recommended  to  those  who 
take  the  regular  course,  as  most  essential. 

Connection  of  Triads  in  Minor  Keys. 

119.  In  taking  up  the  Triads  of  the  Minor  Scale,  the 
principal  point  for  the  beginner  is  to  avoid  the  step  of  an 
Augmented  Second  between  the  6th  and  yth  degrees, 
where  a  good  connection  can  be  made  otherwise.  Being 
a  difficult  interval  to  sing,  the  Augmented  Secord  is  not 
much  used  in  strict  writing.  For  the  same  reason,  all 
Augmented  intervals  (  in  the  progression  of  a  single  part ) 
are  undesirable  for  the  beginner. 

Exercises. 
120.   (a)  Write    the    harmonic    Minor    scale   of    A; 


64  HARMONY  SIMPLIFIED. 

place  the  Roman  Numerals  under  the  notes ;   form  the 
triads  upon  each  degree  as  in  §  91. 

(<5.)  In  the  following  exercises  the  Roman  Nu- 
merals will  be  used  to  indicate  the  triads.  Instead  of 
saying  "  Connect  the  triad  on  A  (  or  on  the  ist  degree) 
with  the  triad  on  D  (  or  the  4th  degree  ),  we  shall  say, 
"  Connect  I  with  iv,"  the  chord  mentioned  first  being 
written  first  and  connected  with  the  other  one. 

( i .)     Connect  i  with  iv ;  with  V ;  with  VI ;  with  11°. 

(  2.  Connect  n°  with  iv ;  with  VI ;  with  V ;  with 
VII°. 

(3.)     Connect  Ilf  with  i ;  V;  VI;  vn°. 

(4.)     Connect  iv  with  i ;  n°;  V;  VI. 

(  5.)     Connect  V  with  i ;  III' ;  vn°. 

(  6.)    Connect  VI  with  I ;  n° ;  III' :  IV. 

(  7.)     Connect  vn°  with  i ;  III" ;  V. 

121.  (c.)  Repeat  in  the  key  of  C  minor:  in  the  key 
of  G  minor :  in  the  key  of  F  minor. 

(d.)  Repeat  the  above  at  the  keyboard,  adding 
other  Minor  keys. 

122.  In  §  41  we  learned  that  the    7th   degree   of  the 
Minor  scale  must  be  raised  by  an  accidental    to    make  a 
Leading-note  to  the  tonic.     This  Chromatic  Alteration 
must  be  indicated  in  the  Bass  of  the  exercises  in  Minor, 
and  is  written  as  follows : 

123.  When  a  sharp,  natural,  or  flat  appears  over  a 
given  Bass  note,  it  is  intended  that  the  note  standing  a  3rd 
above  that  Bass  note  is  to  be  made  sharp,  natural,  or  flat 
as  indicated  by  the  accidental ;  e.  g.,  Fig.  37,  ( a  ),  (  3,  ) 

(c.)  If  the  5th  above  the  Bass  is  to  be  altered,  or 
any  other  interval,  the  figure  representing  the  interval  is 
written  with  the  accidental ;  e.  g.,  Fig.  37,  (</),  (<?), 


HARMONY  SIMPLIFIED. 


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A  diagonal  line  through  a  figure  shows  that  the  inter- 
val represented  by  that  figure  is  to  be  made  sharp;  e.  g., 
(g )»  Fig.  37. 


Exercises. 
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Synopsis. 

124.  Form  a  synopsis  of  the  chapter  as  usual. 

CHAPTER   IV. 

Inversions  of  Triads. 

125.  It  is  not  necessary  that  the  Fundamental  note  (or 
root)  of  a  Triad  should  always  occupy  the  lowest  place.* 
The  Third  or  the  Fifth  can  also  occupy  that  place,  and 
when  this  occurs,  the  chord  is  said  to  be  inverted. 

When  the  Fundamental  is  lowest,  the  chord  is  in  its 
Direct  form. 

When  the  Third  is  lowest,  the  chord  is  in  its  ist 
Inversion. 

When  the  Fifth  is  lowest,  the  chord  is  in  its  2nd 
Inversion.  (  See  Fig.  38.) 

Notice  that  "  Position  "  relates  to  the  Soprano  or 
highest  part,  while  "  Inversion  "  relates  to  the  Bass  or 
lowest  part. 


*  By  inversion  the  Root  is  not  changed,  but  transferred  to  a  higher  part 
The  root  of  a  chord  is  the  Bass  note  only  when  the  chord  is  not  inverted. 


HARMONY  SIMPLIFIED.  fy 

Keyboard  and  Written  Exercises. 
( a.)     Form  various  Triads,  and  show  their  Inrer- 
sions,    as   illustrated  in  Fig.   38.     Avoid  doubling  the 
Third. 


Fig.  38. 


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126.  (  £.)  Write  various  Triads  in  their  several  In- 
versions and    Positions,  using  two   staves.     The  pupil 
should  not  forget  that  Fig.  38  represents  not  three  differ- 
ent chords,  but  three  forms  of  one  and  the  same  chord. 
We  could  not  say  (  because  E  is  in  the  Bass  )  that  the 
form  marked  "  ist  inversion"  in  Fig.  38  is  the  triad  on  E. 
It  is  the  triad  on  C  in  an  inverted  form.     The  note  C  is 
the    fundamental    or   root    from    which    the    chord    is 
derived,  which  note  may  be  placed  lowest  or  highest. 
Therefore,  in  marking  the  triads,  the  inversions  are  to  be 
marked  like  the  direct  form  (the  same  Roman  numerals), 
as  shown  in  Fig.  38.     The  pupil  should  carefully  distin- 
guish between  the  actual  Bass    note,  and   the  root   of 
the  chord.     The  Bass  note  changes  with  each  inversion, 
while  the  real  root  of  the  chord  remains  the  same  for 
all  inversions  and  positions. 

Figuring  Triads. 

127.  In  §  56  the  pupil  learned  to  recognize  intervals 
according  to  their  distance  from  a   lower  note,   and   to 
indicate    the    same   by    figures.     In    a  similar  manner, 
whole  chords  can  be  figured,  by  indicating  the  interval 


68 


HARMON-*  SIMPLIFIED. 


which  each  note  forms  with  the  Bass  or  lowest  note. 
For  example,  if  we  have  a  note  with  the  figures  5  and  3 
over  it : 


we  understand  that  the  interval  of  a  Third  from  the 
note  C  is  required,  and  also  the  interval  of  a  Fifth,  from 
the  same  note.  Thus : 


If  we  have  the  same  note  with  the  figures  6  and  4 
over  it,  we  should  form  the  intervals  of  a  Fourth  and  a 
Sixth  from  that  note  : 


128.     These  intervals  are  not  necessarily  in  the  same 
octave  as  the  Bass  note,  nor  in  the  exact  order  indicated  by 
the  figures,  as  their  arrangement  depends  upon  the  pro- 
gression of  the  parts  in  preceding  chords. 
Exercises. 

(a.)     Figure  the  chords  in  Fig.  38. 

(  6.)  Write  the  scale  of  C  major,  and  form  a  triad 
upon  each  degree.  Write  each  ti'iad  in  its  direct  form 
and  both  inversions,  using  two  staves,  and  writing  in 
four  parts.  Figure  each  chord  thus  produced. 

(c.)  Write  on  an  upper  stafF  (  treble  )  the  chords 
indicated  by  the  figures  over  the  following  Bass  notes» 


HARMONY  SIMPLIFIED.  69 

remembering  the  caution  above  given  in  regard  to  the  notes 
being  neither  in  the  same  octave  as  the  Bass  note,  nor 
in  the  order  expressed  by  the  figures : — 


(</.)      Repeat  the  above  at  the  keyboard. 

To  find  the  Root  of  an  Inverted  Triad. 

129.  A  Triad  is  formed  by  taking  a  note  and  adding 
its  3rd  and  5th  (  see  §  91  )  ;  and  a  triad  so  taken  would 
be  figured  i,  being  in  its    Direct  form.     If  an    inverted 
triad  is  taken,  the  root  of  which   is   not  known,    we  can 
find  the  root  by  continuing  to  invert  till  the  chord  can  be 
figured  3,  i.  e.,  is  in  Direct  form.     When  in  the  Direct 
form,  the  root  is  always  the  lowest  note. 

Exercises. 

Find  the  roots  of  the  following  chords,  and  mark 
each  with  the  proper  Roman  Numeral : — 

130.  Notice  that  the  First  Inversion  of  all  the  triads  is 
figured  3,  and  the  Second  Inversion  |.     From  this  fact  a 
chord  in  its  first  inversion   is  often  called   a  "  Chord  of 
the  Six-Three,"  or  simply  a  «<  Chord  of  the  Sixth";  and 
its  second  inversion  is  called  a  "  Chord  of  the  Six-Four." 

Conversely,  when  a  chord  is  marked  |,  we  know 
the  Bass  note  is  the  Third  from  the  root  (  in  other  words, 
the  chord  is  in  its  first  inversion  )  ;  when  marked  4,  the 
Bass  is  the  Fifth  from  the  root,  the  chord  being  in  the 
second  inversion. 

From  this  (  the  last  preceding  statement )  the  root 
of  the  chord  may  also  be  found. 


HARMONY  SIMPLIFIED. 

Exercises. 
Name  the  roots  of  the  chords  expressed  here: 


(<5.)  Play  the  chords  indicated  by  the  above  Bass 
notes. 

131.     There  are  a  few  conventional  rules  for  Figuring 
chords,  which  the  pupil  must  know  : — 

(a.)  When  no  figures  are  given,  the  Common 
Chord  is  intended. 

(  f>.)  6  means  the  same  as  f;  a  "  chord  of  the  Sixth" 
is  the  same,  therefore,  as  a  "  chord  of  the  Six-three." 

( c.)  A  sharp,  flat,  or  natural,  placed  after  a 
figure,  is  the  same  as  if  placed  before  a  note,  meaning 
that  the  note  indicated  by  the  figure  is  to  be  made  sharp, 
flat,  or  natural,  as  the  case  may  be.  If  a  sharp,  fla4;  or 
natural  is  given  without  any  figure,  the  Third  from  the 
Bass  is  intended.  A  line  through  a  figure,  e.  g.,  &,  is  the 
same  as  a  sharp  after  it. 

(  d.)  The  doubling  of  the  parts,  positions,  leading 
of  the  parts,  etc.,  are  not  indicated  by  the  figuring. 

(  <?•)  Oftentimes  the  figures  of  a  chord  are  not  all 
given,  only  the  characteristic  or  most  important  being 
written,  the  others  being  understood,  as  at  (  b) . 

(y.)  In  writing  a  note  indicated  by  a  figure,  do 
not  consider  the  key  or  signature :  simply  count  the 
degrees  of  the  staff'  (  beginning  with  the  line  or  space 
occupied  by  the  Bass  note  )  just  as  in  §  56. 

(,£".)  If  there  are  two  sets  of  figures  over  a  given 
Bass  note,  it  means  that  the  chord  represented  by  the 
first  set  of  figures  is  to  be  followed  by  the  chord  repre- 
sented by  the  second  set  while  the  Bass  is  held,  the  time* 


HARMONY  SIMPLIFIED. 


value  of  the  Bass    note  being  divided  between  the  two 
chords;  e  g., 


I     i 


Exercises. 
132.     («.)    Applying  the  above  rules,  fill  out  four-pai? 

chords  from  the  following  figured  Basses,  also  marking 
each  chord  with  the  numeral  of  its  root.  (There  is  no 
connection  between  the  successive  chords.) 


(<5.)      Play  the  chords  indicated  above. 

Exercises  in  Part-writing,  introducing  Inversions 

and  Figured  Bass. 

133.  The  mental  processes  described  in  §§103  and 
107,  should  be  carefully  applied  in  the  following  exercises. 
One  question  might  be  added  to  the  process  when  con- 
sidering inversions,  viz.:  "What  is  the  root  of  the 
chord,  and  upon  which  degree  of  the  scale  is  it  ( the 
root  )  ?"  In  every  case  the  chord  should  be  marked  with 
the  proper  Roman  Numeral  (  which  must  appear  as  the 
answer  to  the  above  questions  )  before  proceeding  with 
the  connection  of  chords. 

N.  B.  When  a  chord  appears  successively  in  two 
different  positions  or  inversions,  it  is  obvious  that  the 
rule  in  §  102  (to  keep  the  common  notes  in  the  same 

cannot  be  obeyed,  e.  g., 


HARMONY  SIMPLIFIED, 


This  rule  is  also  occasionally  broken  in  connecting 
two  different  chords,  to  secure  a  good  progression  of 
the  parts.  In  general,  it  will  be  found  that  the  different 
rules  must  yield  one  to  another  as  circumstances  demand. 
(See  §§  161  et  seq.) 

i          R.        6  fi  «  f  § 


2.  J-« 


3    6 


1 


3.          J- 


:  __  ——,  _  —  ^H  _  -r-  H- 


6.          J 


6.  R", 66  6 6 I 


7. 


•36  6        4    S  66 

g»    „   \& 

~^^     C^  ^ 


B 


8. 


-T.  /  » 

-5             X5 

-^    Ib      ^ 

r^"             j 

1 

HARMONY  SIMPLIFIED. 


73 


9. 


e          e 

-(= «, 


11. 


1 


Hidden  Octaves  and  Fifths. 

134.  Hidden  Octaves  and  Fifths  occur  when  two 
parts,  moving  in  parallel  motion,  strike  an  octave  or 
fifth.  If  the  notes  over  which  they  pass  should  be 
written  out,  consecutives  would  appear.  Although  not 
so  disagreeable  as  open  consecutives,  and  not  positively 
forbidden,  Hidden  Consecutives  are  better  avoided, 
unless  by  their  use  a  better  progression  can  be  obtained. 

The  effect  of  Hidden  Octaves  or  Fifths  between  the 
two  outer  parts  is  much  worse  than  between  the  inner 
parts,  or  between  one  inner  and  one  outer  part. 

Where  both  parts  skip  to  the  Octave  or  Fifth,  the 
effect  is  worse  than  if  one  moves  diatonically  to  its 
place.  Hidden  Octaves  and  Fifths  arising  as  shown  in 
Fig.  39  are  freely  permitted. 


Hidden  Octaves. 


Hidden  Fifths. 


Fig.  39. 


-IT' 


The  pupil  should  not  attempt  to  avoid    hidden 
and  8ves  altogether,   but  should  discriminate  in    regard 
to  the  effect,  rejecting  those   that   are   harsh.     Contrary 


74 


HARMONY  SIMPLIFIED. 


motion  will  usually  be  of  assistance  in  avoiding  them, 
but  the  pupil  should  know  that  an  awkward  progression 
of  a  part  is  worse  than  the  hidden  consecutives,  and 
choose  the  lesser  of  two  evils. 

Exercises. 

1.         J-        3        6          6  2.R-    3        6          6  06 


6        $  R-        3.      * 


&    ^g=^==L__j_u  gr; 
\  PF — [-- fjg1  e>  r^-- ^Ff 


II 


6         J 


i 


7.      J- 


8. 


Harmonizing  the  Scales. 

135.  An  excellent  exercise,  at  every  stage  of  advance- 
ment, is  the  practice  of  harmonizing  the  scales  in  every 


HARMONY  SIMPLIFIED.  75 

key,  and  using  as  many  different  chords  and  as  much 
variety  as  the  pupil  may  have  studied  at  the  time.  It 
will  be  noticed  that  every  note  of  the  scale  may  belong 
to  three  different  chords,  and  either  one  of  these  three 
chords  may  be  used  to  harmonize  that  note  if  a  smooth 
connection  with  the  preceding  and  following  chords 
can  be  made. 

The  scale  to  be  harmonized  should  be  written 
sometimes  in  the  Bass  and  sometimes  in  the  Soprano, 
(see  examples  below).  [For  advanced  pupils  it  may 
also  be  written  in  the  Alto  and  Tenor.]  When  written 
in  the  Bass,  it  should  be  observed  that  there  can  be  no 
common  notes  to  connect  two  successive  chords,  unless 
chords  of  the  7th  are  used,  for  which  see  later  chapters. 

Exercises. 
(  a.)     Fill  out  the  four  parts  in  the  following: — 

I.  2. 


f  /(                                             ^    n    Q-\\ 

^i 

I  irTi                 -j  <?  &           \  \               ^ 

^,   <»  &  . 

1  ^r               G>   &                          l-l          -    &   & 

51                  II 

}     Z 

1  CV  f               a         o              II 

II 

m  •      ^                                 L^             -.       '^        ,*3                  II 

II 

•      ^         *y                 ^y                 ^y                 t-^       f^    I  |    ^y        _-      fp 

V                               -^5                                                                                                                            £2 

« 

6                              66 

A3*                                               4' 

3       ^ 
,               Y-*- 

!V                                               II 

IS 

/k^/^l-n                                                                 \\    &      rt        ^ 

II 

r  •  -  \         =>*    &   n                                   5.Z2ZZI5 

S|Z                         &    &    (.3                 II                         g 

2—  «    , 

a*                                ^   {?        II 

&    a                            II             <^ 

66                            &- 

-&- 

5-                                                      6 

6       6 
3                6                                 ^    -<9-                  66 

1 
6 

~J     &     ^             II 

1  •                     —  -j      ^^      ^^                                               \  \               ^-)      ^3      ^^ 

II 

~J            ^^      ^"*                                                                      \  \    ^       "^ 

II 

II 

1.1 

HARMONY  SIMPLIFIED. 


(  £.)  Harmonize  the  ascending  scale  of  C  in  as 
many  ways  as  possible,  using  only  the  triads  with  their 
inversions. 

(c.)      Harmonize  the  descending  scale  similarly. 

(  oT.)  Harmonize  similarly  the  ascending  and  de> 
ecending  scales  in  all  other  keys. 

(  e.)  Advanced  Course.  Harmonize  similarly  the 
Minor  scales. 

(_/".)     Repeat  all  of  the  above  at  the  keyboard. 

Synopsis, 

136.  Write  a  synopsis  of  the  chapter  as  at  the  end  of 
Chapter  III. 

The  Perceptive  Faculties. 
Continued  from  page  40. 

Triads. 

137.  After  teaching  the  pupils  to  recognize  two  tones  sounding 
together,  it  is  but  a  step  further  to  recognize  three  tones.  This 
section  is  merely  a  continuation  of  the  foregoing,  and  may  be  treated 
somewhat  as  follows  : — 

ist  Step,  (a.)  Teacher  sounds  the  note  C,  and  says  :  "  This  tone 

is  Doh.  Write  it  in  the  key  of "  ( mentioning  any  key,  not 

necessarily  the  key  of  C  ). 

(  6.)  Teacher  sounds  E  and  asks,  "  What  is  this  tone?"—  Ans> 
Me.—"  Write  it." — Two  pupils  sing  Doh  and  Me. 

(  c.)  Teacher  sounds  G  and  asks,  "What  is  this  tone  ?"—  Arts. 
Soh.  —  "  Write  it."—  Third  pupil  sings  Soh.  Three  pupils  sing  the 
three  notes  together. 

(</.)  While  the  chord  is  being  sounded,  the  teacher  says, "Re- 
mainder of  the  class  sing  Me  ;  (  sing  Soh ;  sing  Doh  ).  Which  note 
is  highest  ?—  Which  is  lowest  ?—  Which  between  ?" 


HARMONY  SIMPLIFIED. 


77 


In  this  way  the  pupils  learn  to  hear  and  distinguish  the  individ- 
ual notes  from  the  mass  of  sound,  for  as  soon  as  they  have  sung  them 
a  few  times  while  the  chord  is  sounding,  they  will  be  able  to  hear 
the  individual  tones,  and  thus  recognize  the  component  parts  of  a 
chord. 

The  teacher  should  not  confine  himself  to  the  triad  on  C,but 
may  take  any  Major  triad  in  the  middle  of  the  keyboard  or  of  the 
voices.  The  note  which  is  represented  by  Doh  should  always  be 
announced,  to  give  a  starting-point. 

138.  znd  Step.  Having  trained  the  pupils  to  recognize  the  notes 
of  the  triad  by  the  above  and  other  exercises  which  his  ingenuity  or 
the  necessities  of  the  case  may  suggest,  the  teacher  should  proceed 
to  train  the  pupils  to  recognize  the  different  positions  of  the  Triad. 

Process: — (a.)  Teacher  sounds  triad  C-E-G,  and  asks,  "What 
are  the  syllabic  names  of  these  tones  ? —  Which  is  highest  ?  —  Which 
lowest  ?" 

(b.)  Teacher  sounds  same  triad,  but  in  position  of  the  Octave, 
repeating  the  change  to  make  it  forcible,  as  follows : 


and  asks,  "  Which  note  is  highest  in  the  last  chord  ?  —  Which  is  low- 
est ? — Which  between  ?"  Require  the  pupils  to  sing  the  notes  one  by 
one,  using  the  syllabic  names,  while  the  chord  is  sounding.  Also 
ask  them  to  fix  their  attention  strongly  on  one  individual  note  in  the 
chord,  while  the  teacher  plays  the  chord,  and  try  to  hear  it,  i.  e., 
to  individualize  the  note  from  the  chord,  and  thus  cultivate  the 
perceptions. 

In  the  same  manner  the  remaining  positions  should  be  taught. 

139.     yd  Step.     Chords  of  four  tones. 

(a.)  Let  three  pupils  sing  the  triad  C-E-G.  Teacher  sounds 
C  (  3rd  space,  treble  )  and  asks,  "  What  is  this  note  ?" —  Ans.  Doh.— 
"Which  Doh?" — Ans.  Octave  above  the  first  Doh. —  Fourth  pupil 
sings  upper  Doh.  Four  pupils  sing,  forming  the  chord,  while  re- 
mainder of  class  sing  single  tones  as  before.  Teacher  asks,  "  Which 
note  is  highest?  —  Which  is  lowest? — Which  is  intermediate?— 
Which  note  is  doubled  ?" 

NoTfi.  The  piano  may  be  used  to  produce  the  chord,  but  it  is 
far  preferable  to  have  it  sung. 

Proceed  as  above  with  other  two  positions. 


HARMONY  SIMPLIFIED. 


140.     4/4  Step.    Inversions. 

Play  the  following,  asking  questions  as   before,  concerning  the 
highest  and  lowest  notes,  etc.: 


'  '  a 

a 

(3)   g  — 

—  <g  

J    .g. 

f\  • 

SEEzEE 

—  ^  

S3 

Then  play  the  passage  next  given,  calling  attention  to  the  move 
ment  of  the  bass,  and  to  the  different  musical  effects  of  the  different 
inversions,  wrong  doubling  at x,  etc.  Repeat  with  other  Major 
chords,  ".sking  questions  as  above. 

X 


1 


141.     tfh  Step.    Minor  Triads. 
Play : 


calling  attention  to  the  different  effect  of  the  Minor,  showing  how  it 
differs  from  the  Major,  asking  questions  as  above,  etc.  Take  in 
succession  the  Minor  triads  of  the  key  of  C  ( also  other  keys  ),  and 
question  in  regard  to  highest  and  lowest  notes,  etc. 

142.    6th  Step.    Progression  of  apart. 

Play  little  progressions  where  a  single  part  moves,  requiring  the 
class  to  recognize  which  part  moves  and  what  the  progression  is. 
( The  answers  should  be  in  syllabic  names,  and  the  notes  wrtten  as 
recognized.)  To  illustrate,  play  : 


HARMONY  SIMPLIFIED. 


Process :  —  First  name  the  notes  in  the  first  chord ;  ascertain  the 
position  and  inversion,  and  write  the  notes.  Then  study  the  pro- 
gression. 

Next  take  up  examples  where  two  parts  move  without  change  of 
chord;  e.  g., 


Lack  of  space  prohibits  the  multiplication  of  these  simple  ex- 
amples, which  can  be  taken  from  many  sources  or  invented  by  the 
teacher.  Many  examples  should  be  studied  before  proceeding. 

143.  "jth  Step.     Progression,  of  parts  with  change  of  chords. 

(a.)  Without  Inversions:  Give  some  examples,  if  necessary 
selecting  from  the  first  exercises  in  part-writing  (§  113,  etc.),  calling 
especial  attention  to  the  progression  of  the  Bass ;  for  if  that  can  be 
ascertained,  the  fundamental  of  each  chord  is  clear,  and  with  it  the 
chord  itself,  though  the  position  may  remain  in  doubt.  (  The  posi- 
tion will  be  discovered  by  requiring  the  pupils  to  sing  the  notes  of 
the  chord,  using  the  syllabic  names.) 

Notice  also  the  progression  of  the  Soprano,  whether  up  or  down. 

The  first  exercises  should  consist  of  but  two  chords —  one  pro- 
gression,—  and  should  illustrate  the  progression  from  the  Tonic  to 
the  Dominant  or  Sub-dominant,  after  which  the  progression  from  the 
Tonic  to  the  remaining  degrees  of  the  scale  may  be  studied,  and  later 
exercises  may  be  extended  to  take  in  several  progressions.  It  is  of 
especial  importance  that  the  exercises  be  carefully  written. 

144.  ( b.)     Progressions  with  Inversions. 

This  is  more  difficult  than  the  preceding,  and  requires  patience 
OB  the  part  of  both  teacher  and  pupil.  At  first  give  chords,  the  nat- 


0  HARMONY  SIMPLIFIED. 

oO 

oral  progression  of  which  can  be  easily  traced,  as  for  example  those 
given  here.    Those  progressions  are  best  which  have  some  tied  notes. 


as  the  attention  can  be  concentrated  on  one  or  two  moving  parts. 
Simple,  well-known  harmonies  only  should  be  used,  leaving  the  mor? 
difficult  ones  till  a  later  period.  The  teacher  should  constantly  lead 
and  direct  the  perceptions  by  questions  as  illustrated  above.  Ea<i» 
step  should  be  expressed  in  notes. 

145.  It  will  be  advantageous  at  this  point  for  the  pupil  to  refer  tt 
the  exercises  he  has  already  written,  and  try  to  think,  from  lookine 
at  the  progressions,  how  they  would  sound.  Indeed,  he  should  never 
look  at  a  chord  without  trying  to  realize  its  effect. 

NOTE.  The  treatment  of  the  Perceptive  faculties  is  here  given, 
not  as  a  complete  exposition  of  the  subject,  but  merely  as  a  suggestive 
outline,  to  be  expanded  and  adapted  by  the  teacher  to  the  needs  of 
individual  cases. 

Transposition. 

146.  The  pupil  will  gain  a  practical  idea  of  Trans- 
position through  the  exercises  used  in  developing  the 
perceptive  faculties,  if  the  teacher  will  vary  the  keys  in 
which  the  pupil  writes  what  he  hears.  For  example,  the 
teacher  may  say  when  beginning  an  exercise,  "  This 
tone  is  Doh  "  (  striking  some  note  )  ;  "  write  in  thfe  key 
ofG."  After  a  few  moments  he  may  say,  'without 
changing  the  pitch  of  Do  A,  "  Write  in  the  key  of  F" ; 
and  the  pupils  will  soon  find  that  they  can  as  well  express 
the  relations  of  the  notes  to  each  other  in  one  key  as 
in  another. 


HARMONY  SIMPLIFIED.  8 1 

IMPORTANT  JNOTE. 

In  this  book  the  chords  of  the  Dominant  yth,  Diminished  yth, 
Major  and  Minor  gth,  and  the  Augmented  3»  4,  and  5,  are  treated  ai 
different  forms  of  the  same  chord,  having  the  same  root,  same  disso- 
nant intervals,  and  same  resolution.  In  learning  the  natural  reso- 
lution of  dissonant  intervals  in  general,  the  proper  resolution  of 
all  these  chords  is  learned,  thus  simplifying  and  systematizing  the 
subject  to  a  remarkable  degree.  Therefore,  study  Chapter  V 
thoroughly,  repeating  again  and  again,  if  necessary,  till  the  subject  is 
reaily  clear. 


CHAPTER  V. 

CHORDS  OF  FOUR  NOTES  :    THE  CHORD  OF  THE  SEVENTH. 

its  Construction. 

147.  As  stated  in  §  90,  the  whole  system  of  chords  is 
a  process  of  building,  or  adding  upper  notes  to  some 
note  considered  as  a  Root  (  Foundation,  or  Fundamental)  . 
The  various  triads  were  formed  by  adding  a  3rd  and  a  5th 
to  such  a  Root-note.  If  we  add  not  only  the  3rd  and  the 
5th,  but  also  the  interval  of  a  7th  to  the  Root-note  or 
Fundamental,  we  shall  have  a  Chord  of  the  Seventh. 

To  illustrate,     /£  i$     :  represents   the   root   G  with 


its  3rd  and  5th  forming  a  triad.  If  the  interval  of  a  7th 
(  from  G  )  is  also  added,  we  have  /£  *%—•>  called  a 

Chord  of  the  Seventh.  (  It  may  be  noticed  in  reference 
to  this  building-process,  that  each  note  is  at  the  interval 
of  a  3rd  —  either  Major  or  Minor  —  from  the  note  next 
below.  In  the  following  chapters  it  will  be  seen  that  this 


g,  HARMONY  SIMPLIFIED. 

same  rule  of  placing  the  successive  notes  a  3rd  apart  is 
followed  in  forming  chords  of  the  Ninth  ;  also  in  what  are 
called,  by  some  theorists,  the  chords  of  the  Eleventh  and 
the  Thirteenth.) 

As  the  character  of  Triads  differs  according  to  the 
character  of  the  component  intervals,  (Major,  Minor, 
etc.,  see  §  93,)  so  the  character  of  the  Chords  of  the 
Seventh  must  differ. 

Exercises. 

148.  (  a.)  Write  chords  of  the  7th  upon  every  note 
of  the  Major  scales  of  C,  G,  F,  and  D,  describing  the 
character  of  the  triad  as  in  §  93,  and  indicating,  on  a  sep- 
arate line,  the  character  of  the  yth.  For  example,  form- 
ing the  chord  of  the  yth  on  the  third  degree  of  the  scale 
of  C,  it  would  be  described  as  in  Fig.  40. 


Fig.  40. 


1 


in  with 
Minor  Seventh. 


The  Roman  Numeral,  being  small,  indicates  that  the 
triad  is  Minor.  The  character  of  the  7th  is  plainly 
expressed. 

(  6.)  Write  chords  of  the  7th  upon  every  note  of 
the  Minor  scales  of  A,  E,  D,  and  B,  indicating  the  char- 
acter of  the  triad  and  the  7th  as  above. 

(c.)      Repeat  all  of  the  above  at  the  keyboard. 

149.  The  pupil,  while  writing  the  above,  should 
notice  the  following  : — 

(  i.)  That  some  of  the  chords,  particularly  in  the 
Minor  keys,  sound  so  badly  that  they  could  not  be  used. 

(2.)  That  the  chord  of  the  7th  formed  upon  the  5th 
degree,  the  Dominant,  is  alike  in  Major  and  Minor, 


HARMONY  SIMPLIFIED.  83 

and  is  not  only  the  most  agreeable  one,  but  is  the  only 
one  having  a  Major  3rd  and  Minor  7th. 

(3.)     That  none  of  the  chords  of  the  7th  are  satis- 
factory to  rest  upon,  but,  like  the  Augmented  and  Di- 
minished intervals  and  triads,  seem  to  require  something  to 
come  after  them  to  create  a  feeling  of  repose, 
(a.)  (6.) 


Fig.  4 1 . 


For  example,  the  chord  («),  in  Fig.  41,  although  it 
sounds  well,  is  evidently  not  satisfactory  to  dwell  upon, 
or  to  use  as  the  final  chord  of  a  composition,  as  it  seems 
to  suggest  something  which  should  follow  to  make  it 
complete.  Notice  that  the  chord  marked  (  b  )  gives  this 
sense  of  completeness  and  repose. 

150.  This  leads  us  to  consider  that  all  chords  may  be 
divided,  with  respect  to  this  quality  (  repose  or  the  lack 
of  it),    into  two  kinds:    Independent   chords,   or  those 
which  are  satisfactory  to  pause  upon ;    and  Dependent 
chords,  or  those  which  demand  that  some  chord  should 
follow   to   establish   repose.      This   classification    corre- 
sponds with  the  division  of  intervals  into  Consonant  and 
Dissonant  (  see  §  75  ) '  ^or  those  chords  containing  conso- 
nant   intervals    exclusively   are    Independent,     while 
those  containing    even  one  dissonant  interval  are  De- 
pendent chords. 

151.  This  demand  on  the  part  of  a  Dependent  chord 
to   be  followed  by  something  reposeful,  is  satisfied  if  a 
consonant   chord   succeeds   it.     The  process  of   passing 


84  HARMONY  SIMPLIFIED. 

from  a  Dependent  chord  to  one  that  is  consonant  (  Inde- 
pendent )  is  called  "resolving"'*.,  and  the  chord  to 
which  it  progresses  is  called  the  "  chord  of  resolution" 
It  is  necessary  to  resolve  dissonances,  not  only 
because  they  are  unsatisfactory  to  rest  upon,  but  also  be- 
cause there  are  tendencies  on  the  part  of  certain  inter- 
vals contained  in  them,  and  of  certain  notes  of  the 
scale,  to  progress  in  definite  directions* 

The  Principle  of  Tendencies:  Melodic 

Tendencies. 

152.  (  a.}  This  tendency  of  certain  notes  of  the  scale 
to  progress  in  definite  directions  may  be  illustrated  by  sing- 
ing the  Major  scale  up  to  and  including  the  7th  degree,  then 
suddenly  pausing  without  singing  the  regaining  (8th) 
degree.  By  thus  pausing,  a  sense  of  incompleteness  will 
be  felt, —  a  desire  for  the  delayed  note.  Thus  it  is  clear 
that  the  7th  degree  has  a  strong  tendency  to  progress  to 
the  8th  degree,  which  is  the  Tonic,  or  most  perfect 
resting-place  in  the  whole  scale.  On  account  of  this 
marked  tendency  toward  the  tonic  (or  its  octave),  the  7th 
degree  of  the  scale  is  called  the  Leading-note. 

(6.)  Similar  experiments  will  show  that  the  3rd 
degree  of  the  scale  has  a  distinct  tendency  to  ascend, 
though  the  tendency  is  not  so  strong  as  in  the  case  of  the 
7th  degree ;  and  that  the  4th  degree  tends  downward. 

(  c.)  An  accidental  sharp  tends  to  continue  upward, 
and  an  accidental  flat  downward.  (  N.  B.  When  a  nat- 
ural is  used  to  raise  a  note  already  flatted  by  signature 
or  otherwise,  it  is  like  a  sharp  in  its  effect,  and  has  the 
same  tendency  to  ascend.  Likewise,  when  a  natural  is 


*  In  fact,  the  reason  that  some  chords  are  unsatisfactory  to  pause  upon  is 
simply  because  certain  intervals  and  notes  have  the  above-mentioned  tenden- 
cies ;  for  while  perfectly  agreeable  to  listen  to,  they  point  unmistakably  toward 
something  which  is  to  follow. 


HARMONY  SIMPLIFIED.  85 

used  to  depress  a  note  already  sharped,  it  is  like  a  flat  iu 
its  effect,  and  has  the  same  tendency  to  descend.)  Notes 
having  a  tendency  to  progress  in  a  particular  direction, 
are  called  Tendency-notes. 

Tendency  of  Continuity. 

153.  A  tendency  to  progress  in  any  desired  direction 
may  be  given  to  a  note,  or  a  natural  tendency  counteracted, 
by  approaching  that  note  from  a  contrary  direction. 
Thus,  if   it    is  desired  to  have  the  yth  degree  progress 
downward,  it  can  be  done  by  approaching  it  from  above : 

^Tfc-t — 0      &  This   might   be  called  the  Tendency 

oj  Continuity,  i.  e.,  to  continue  in  a  given  direction 
after  having  started. 

Harmonic  Tendencies. 

1 54.  An  Harmonic   Tendency  is  the  tendency  of  a 
dissonant  interval,  or  of  the  notes  forming  it,  to  progress 
in  certain  definite  directions.     It  is  apparent  that  the  nat- 
ural (Melodic  )  tendencies  of  the  above  named  Tendency- 
notes  are  not  so  strong  but  that  they  may  be  overcome 
by  the  tendency  of  Continuity.     But,   when  this  natural 
tendency  is  heightened  by  the  presence  of  dissonant  in* 
ter-vals,  the  demand  for  progression  is  quite  unmistakable. 
Let  us  examine  the  effect  of  dissonant  intervals  upon  the 
tendency  to   progress. 

(  i  )      Play  the  following  and  pause: 


T 

the  ear  will  then  demand   that  GJ   shall   progress  to   A 
This  is  caused,  first,  by  the  fact  that  in  touching  G#  we 
have  started  on  the  road  from  G  to  A,  and  having  com* 


86  HARMONY  SIMPLIFIED. 

pleted  half  the  distance  ( theoretically  a  little  more  than 
half) ,  it  is  only  natural  to  desire  to  continue  to  the  desti- 
nation. It  would  be  useless  to  go  half-way,  and  then  turn 
back.  (See  §  152,  c.)  Secondly,  it  is  caused  by  the 
fact  that  we  have  at  x  a  perfect  5th,  followed  by  an  aug- 
mented 5th.  The  perfect  5th  has  been  made  larger  by  a 
sharp,  and  it  would  be  expected  to  develop  into  something 
else  instead  of  retreating.  Thus  it  is  apparent  that  the 
combined  influences  at  work  must  create  a  demand  for  a 
chord  to  follow  any  dependent  chord. 

(2.)  Again,  striking  the  interval  at  («),  Fig.  42, 
we  find  a  strong  tendency  to  progress  to  the  interval  at  (<$.) 
This  is  caused  by  the  same  tendency  of  an  augmented 
interval  (  here  an  augmented  4th  )  toward  a  further  di- 
gression of  the  parts. 

(a.)        (b.) 


Fig.  42. 

(  3.)  On  the  other  hand,  if  we  take  a  Normal  inter- 
val and  diminish  it,  there  is  a  strong  tendency  to  still  fur- 
ther contract,  as  in  Fig.  43,  where  (  a  )  is  the  Normal 
interval,  (  b  )  the  diminished  and  (  c  )  the  result  of  the 

tendency  toward  further  contraction. 
(a.)         (b.)       (c.) 


Fig.  43. 

These  are  illustrations  of  Harmonic  Tendencies. 

To  formulate  the  illustrations  in  Figs.  42  and  43, 
the  following  is  given  : — 

All    Augmented  intervals   tend  toward  further 
expansion. 

All  Diminished  intervals   tend  toward  further 
contraction. 

NOTE.    This  law  is  a  direct  result  of  the  principles  stated  in 
§§152  (<r)and  153. 


HARMONY  SIMPLIFIED.  87 

• 

Advanced  Course. 

From  the  above  it  will  be  seen  that  there  is  an  exceedingly  close 
connection  between  Melodic  and  Harmonic  Tendencies.  In  fact,  an 
Harmonic  Tendency  might  be  defined  as  the  result  or  effect  produced 
by  the  presence  of  a  Melodic  Tendency-note  in  a  dissonant  interval. 
The  dissonance  serves  to  heighten  and  emphasize  the  tendencies  of  the 
single  tones.* 

Regular  Course. 

155.  In  §  75  it   was   stated,   that  Dissonant  intervals 
were  so  named  on  account  of  their  unrestful  effect,  requir- 
ing or  pointing  to  some  other  interval  to  follow.      It  may 
also  be  stated,   that  the  natural  tendency  of  a  dissonant 
interval  is  to  progress  to   the  nearest  consonant  interval 
belonging  to  the  key,  the  tones  moving  according  to  the 
principles  shown  in  §§  152  —  154. 

As  chords  are  made  up  of  intervals,  it  follows,  that 
dissonant  (  i=  e.,  Dependent)  chords  are  those  which  contain 
dissonant  intervals,  and  the  natural  resolution  of  a  chord  depends 
upon  the  tendencies  of  the  dissonant  intervals  contained  in  it. 

Now,  let  us  apply  our  knowledge  of  Tendencies  to 
the  Chord  of  the  Dominant  Seventh. 

Chord  of  the  Dominant  Seventh:   Resolution  of 

Dissonances:  Application  of  the  Principles 

of  Tendencies:  Cadencing  Resolution. 

156.  The  chord  of  the  7th  which  is  founded  on  the 
5th  degree  of  the  Major  and  Minor  scales,   has  already 
been  mentioned  as  being  the  most  agreeable  of  all  chords 
of  the  Seventh,   and  is  peculiar  in  being  the    only   one 
having  a  Major  3rd  and  a  Minor  7th.     Having  a  very 
close  relationship  with  the  chord  on  the  Tonic  (  see  §§158 


*  A  consonant  interval,  being  restful  in  its  nature  (  see  5  75  ),  would  serve 
\nhide  rather  than  to  emphasize  the  melodic  tendencies  of  the  single  tones. 


88  HARMONY  SIMPLIFIED. 

• 

and  266  ) ,  this  chord  plays  an  important  part  in  forming 
a  key,  and  is  called  the  chord  of  the  Dominant  ("ruling") 
Seventh.  The  pupil  is,  of  course,  already  familiar  with 
this  chord,  as  it  is  used  very  frequently. 

157.  According  to  the  principles  stated  in  §  155,  it  be- 
comes necessary  to  examine  the  structure  of  the  chord  of 
the  Dominant  yth,  and  find  its  dissonant  intervals,  if  we 
would  understand  its  resolution.  Taking  the  chord  in  the 
order  in  which  it  is  constructed,  let  us  examine  it  in  detail. 


From  G  to  B  is  a   Major  2,rd,  which  is  a 

consonance ;  from  G  to  D  is  a  Perfect  5th,  which  is  also 
a  consonance ;  from  G  to  F  is  a  Minor  yth,  and  here  we 
find  the  first  dissonant  element,  for  we  have  learned  that 
sevenths  are  dissonances  (see  §  75)-  Again,  starting  from 
the  second  note  of  the  chord,  B,  we  find  that  from  B  to  D 
is  a  Minor  3rd,  a  consonance :  from  B  to  F  is  a  dimin- 
ished 5th,  forming  a  dissonance.  Here,  then,  is  the 
second  dissonant  element.  Further,  starting  from  the 
third  note  of  the  chord,  from  D  to  F  is  a  Minor  3rd,  a 
consonance. 

We  have  learned  that  the  character  of  a  chord  (  con- 
sonant or  dissonant)  depends  upon  the  character  of  the 
intervals  contained  in  it.  Therefore,  we  see  that  the  reason 
this  chord  is  dissonant  is,  that  it  contains  the  dissonant  inter- 
vals of  a  Minor  7th  from  G  to  F,  and  of  a  Diminished 
5th  from  B  to  F.  (  Notice  that  if  the  note  F  were  absent, 
there  would  be  no  dissonant  intervals;  i.  e.,  the  addition 
of  a  7th  to  the  triad  changes  an  Independent  Triad  to  a 
Dependent  Seventh-Chord. ) 

The  tendencies  of  these  dissonant  intervals,  in  regard 
to  resolution,  are  as  follows : — The  tones  of  the  Dimin- 
ished 5th:  FfeEE^E::  tenc*  to  aPProach  (§154),  F 


HARMONY  SIMPLIFIED. 


89 


tends  also 


remains 


progressing  downward  to  the  next  step,  and  B  upward 

The  minor  7th :  h/L-     — 
Hk)       & 
o 

to    converge,    F   passing   downward,   while 
stationary,  or  may  progress  upward ;  t 

In  addition  to  tnese  Harmonic  tendencies,  we  must 
also  consider  the  Melodic  tendencies  mentioned  in  §  152. 
Here  we  have  the  Leading-note,  B,  tending  strongly  up- 
ward, and  the  fourth  degree  of  the  scale,  F,  tending 
slightly  downward.  As  these  Melodic  tendencies  agree  per- 
fectly with  the  Harmonic  tendencies,  the  natural  resolution 
of  the  chord  becomes  clear.  Let  it  be  noticed,  that  the 
tones  without  any  special  tendency  may  progress  either 
upward  or  downward,  or  may  remain,  as  may  be  neces- 
sary either  to  avoid  consecutive  5ths  or  Sves,  or  to  Jill  up 
the  chord  of  resohition  to  advantage.  In  accordance 
with  the  natural  resolution  of  the  dissonant  intervals,  the 
resolution  of  the  chord  is  as  follows : — 


In  the  different  positions  of  the  chord,  although  the 
notes  may  change  their  mutual  intervallic  relationship (e.  g., 
by  inverting  the  intervals),  the  tendencies  and  progres- 
sions of  the  individual  tones  remain  quite  the  same  as 
above  described.  Fig.  44  shows  the  different  positions  of 
the  chord  of  the  Dominant  7th,  with  their  natural  resolu' 


<jO  HARMONY  SIMPLIFIED. 

tions.  Notice  that  in  every  position  the  Leading-note,  B< 
progresses  upward,  while  F,  the  4th  degree  of  the  scale, 
moves  downward.  Notice,  also,  that  the  interval  of  a 
Diminished  5th,  B  —  F,  at  (  a  )  and  (£),  Fig.  44,  ap- 
pears inverted,  i.  e.,  an  Augmented  4th,  F  —  B,  at  (  c  ) 
and  (^),  tne  augmented  interval  expanding  for  its 
resolution,  and  the  Diminished  contracting ;  'while  the 
progression  of  the  individual  tones  remains  the  same 
( i.  e.,  B  moves  to  C,  and  F  to  E,  in  both  cases). 


Fig.  44. 


N.  B.  The  natural  resolution  of  these  intervals  is 
always  the  same',  therefore,  wherever  we  find  them, 
whether  in  chords  of  the  Dominant  7th,  Diminished  yth, 
Minor  pth,  or  Augmented  6th,  we  may  expect  them  to  re- 
solve just  the  same.  When  they  do  not  follow  this  natu- 
ral resolution,  there  is  a  reason  for  it,  explained  in  §§  161 
to  169,  and  192  to  198;  but  the  principle  remains  un~ 
changed. 

The  Natural  or  Cadencing  Resolution. 

158.  In§  156  we  noticed  the  close  relationship  of  the 
Chord  of  the  Dominant  Seventh  to  the  Tonic  triad.  It 
will  now  be  observed,  that  the  tendencies  of  the  tones  F 
and  B  in  Fig.  44  are  toward  E  and  C  respectively, 
•which  are  parts  of  the  tonic  triad,  while  G  may  re- 
main, thus  completing  the  triad.  When  the  chord  of 


HARMONY  SIMPLIFIED. 


the  Dominant  seventh  is  resolved  thus  to  the  Tonic  Triad, 
the   resolution    is   called   the    Cadencing    Resolution.* 

If  the  above-mentioned  tendencies  are  respected,  and 
the  remaining  parts  are  led  as  smoothly  as  possible,** 
avoiding  unnecessary  skips  and  consecutive  5ths  and  Sves, 
the  pupil  will  not  need  detailed  rules,  other  than  those  al- 
ready given,  for  the  following  exercises.  One  or  two 
hints  may,  however,  be  of  service. 

Remember  that  it  is  better  to  double  the  Fundamen- 
tal or  5th  of  a  chord  than  the  jrd.  Sometimes  the  5th  of 
the  final  chord  must  be  omitted  to  secure  a  good  leading 
of  the  parts,  another  note  being  doubled  in  its  stead ;  or 
the  5th  of  the  chord  of  the  Dominant  Seventh  may  not  ap- 
pear, for  the  same  reason.  (  This  also  applies  occasionally 
to  the  triads.) 

Exercises. 

(a.)  Fill  out  the  chords  marked  I  in  Fig.  45,  lead- 
ing the  parts  upward  or  downward  as  indicated  by  the 
diagonal  lines;***  and  explain  the  tendencies  as  above. 


Fig.  45. 


:0 


V7          i        v?        I        V7          IV          I 
Form  Cadencing  resolutions  of  the  chord  of 


*  It  should  be  observed,  that  the  triad  on  C  is  the  resolution  of  the  Chord 
of  the  Seventh  upon  G,and  that  C  is  a  4th  higher  than  G.  Therefore,  when 
any  Chord  of  the  Seventh  resolves  to  the  Triad  a  4th  higher  (  or  a  $th  lower  ), 
this  is  said  to  be  a  Natural  or  Cadencing  resolution.  (See  §  190.) 

**  The  pupil  should  carefully  note  the  difference  between  progression  and 
resolution.  A  resolution  is  a  progression,  but  is  influenced  by  the  presence 
of  dissonant  intervals,  and  is  therefore  not  free.  A  resolution  implies  the  pres- 
ence of  a  dissonance  in  the  previous  chord. 

***  In  the  natural  resolution,  the  dissonant  tones  ( and,  in  fact,  all  the 
tones)  must  move  dirtonically.  ( See  §  3,  foot-note,  and  §  44 ). 


HARMONY  SIMPLIFIED. 


the  Dominant  Seventh  in  four  positions,  in  the  key  of  F ; 
in  the  key  of  G ;  of  Bt7;  of  A;  of  D ;  of  FJ.  Designate 
the  tendency-notes  by  heavy  lines  indicating  the  direction 
in  which  they  resolve,  as  shown  in  Fig.  45. 

(c.)      Repeat  the  above  at  the  keyboard,  continuing 
till  facility  is  gained  in  every  Major  and  Minor  key. 

159.  In  the  first  foot-note  of  §   158,  it  is  shown  that 
a  chord  of  the  Dominant  yth  resolves  to  the  triad  a  4th 
higher.     Conversely,  if  we  would  find  that  Chord  of  the 
Dominant  yth  which  shall  resolve  to  any  desired  triad,  we 
need  merely  to  look  for  the  note  a  4th  lower  than  the  Root 
of    the    triad ;   and,   having  the  root,  we    can  build  the 
chord  as  shown  in  §  147. 

Exercises. 

Name  the  Root  of  the  chord  of  the  Dominant  7th 
which  shall  resolve  to  the  triad  of  D ;  write  the  whole 
Chord  of  the  7th  and  resolve  it. 

Name  the  Root  and  write  the  Chord  of  the  7th  which 
shall  resolve  to  the  triad  of  A ;  of  G ;  of  Bt? ;  of  Ffl ;  of 
A# ;  of  B ;  of  F ;  etc. 

Exercises. 

1 60.  In  the  following  exercises,  the  Chord  of  the  7th 
will  be  indicated  by  the  figure  7  over  the  bass. 

T>      a  « 

^^       6 6 


& 


2. 


-&-      C         67  6         4         7 


J-      4. 


HARMONY  SIMPLIFIED. 


The  Principles  of  Part-leading:  "  Influences," 
Combined  and  Opposed. 

161.  It  has  been  said  that  the  rules  of  Harmony  were 
made  only  to  be  broken,  and  that  every  rule  has  more  ex- 
ceptions than  applications.  It  would  seem  better,  there- 
fore, to  review  the  principles  from  which  the  rules  are 
derived,  and  thus  gain  a  sound  judgment  in  regard  to  the 
leading  of  the  parts,  which  must  ultimately  replace  any 
rules  that  could  be  given. 

The  sources  of  the  rules  which  are  commonly  given, 
are  found  in  the  necessity  of  considering  the  following 
•points  in  order  to  produce  good  effect  in  part-writing: 

(  i.)     The  Harmonic  effect  of  the  four 
parts  together. 

(2.)     The  Melodic  effect  of  the  indi- 
vidual parts. 

(3.)  The  Tendencies  of  certain  notes  of  the  scale, 
and  of  various  dissonant  intervals;  i.  e.,  the  Melodic  and 
Harmonic  Tendencies.  (See  §§  152  to  155.) 

(4.)     The  bad  effect  of  Consecutive  5ths  and  8ves. 

(.5.)     The  bad  effect  of  doubled  3rds.* 

(6.)     The  Prominence  of  Outside  Parts.** 

(  7.)  The  desirability  of  Connection  between  suc- 
cessive chords. 

(8.)  The  arrangement  of  the  notes  in  a  chord;  i.  e., 
their  distance  apart.*** 


(See  §97.) 


»r  **:  ***•  See  the  following  paragraphs. 


94 


HARMONY  SIMPLIFIED. 


The  above-mentioned  points  may  be  called,  for  con- 
venience, "  Influences  "  which  affect  or  control  the  lead- 
ing of  the  parts.  Sometimes  these  various  Influences 
agree,  or  combine  to  demand  the  same  progression  ;  some- 
times they  oppose  one  another. 

Notes  upon  the  Preceding. 

162.  *By  doubling  the  3rd  a  certain  dissonant  overtone  (See  §  90; 
and  Note,  p.  44)  is  brought  into  prominence,  making  the  chord  some- 
what rough  in  effect.    Therefore  it  is  not  well  to  double  the  3rd  with- 
out some  definite  reason. 

Furthermore,  in  the  Tonic  triad,  and  also  in  the  Dominant  triad 
or  Chord  of  the  7th,  chords  which  appear  very  frequently,  the  3rd  is  a 
tendency-note.  (See  §152.)  Now,  it  will  be  seen  that  tendency-notes 
should  never  be  doubled,  if  possible  to  avoid  it,  as  the  result  must  be 
either  consecutive  8ves  or  the  contradiction  of  the  tendency  by  one  of 
the  notes.  Therefore,  where  the  3rd  is  a  tendency-note,  it  should  not 
be  doubled.  Where  it  is  not  a  tendency-note,  it  may  be  freely  doubled 
if  thereby  a  better  leading  of  the  parts  is  obtained.  (  The  chief  Ten- 
dency-notes (  Melodic  )  of  a  scale  are  the  3rd  and  7th.  When  the  3rd 
of  a  chord  happens  to  be  one  of  these  notes,  it  is  better  not  doubled.) 

163.  **It  will  be  observed,  that  the  Soprano  and  Bass  parts  are 
more  conspicuous  than  the  inner  parts.     Therefore,  that  which  might 
be  allowed  in  the  inner  parts  may  be  found  very  disagreeable  —  and 
consequently  be  forbidden,  —  when  occurring  in  the  outer  parts.     In- 
cluded in  the  above  are  found  most  frequently  the  two  points  of 

( a.)    Disregarded  tendencies  :  e.  g., 

(a.)  Bad.  (b.)  Good. 


Fig.  46. 


G> L 


1 


At  ( a),  Fig.  46,  the  upward  tendency  of  the  Leading-note,  B,  is 
disregarded,  it  being  led  down  to  G,  with  very  bad  effect.  At  (  b )  the 
same  thing  is  done,  but  in  an  inner  part.  The  effect  here  is  very  good, 
as  the  Alto,  an  inner  part,  is  less  prominent  than  the  Soprano,  and  as 
the  note  to  which  the  Leading-note  would  have  progressed  is  still 


HARMONY  SIMPLIFIED. 


95 


found  in  the  last  chord.  Again,  by  the  progression  of  the  Alto  Lead- 
ing-note down  to  G,  the  last  chord  has  the  5th  which  would  other- 
wise be  lacking. 

(t>.)     Hidden  Consecutives :  e.  g., 
(a.) 


Fig.  47. 


1 


The  progression  at  (  a  ),  Fig.  47,  is  too  harsh  to  be  effective,  the 
hidden  consecutives  appearing  in  the  outer  parts  ;  but  the  progression 
at  (  b  )  is  much  more  agreeable,  as  the  hidden  consecutives  are  be- 
tween one  inner  and  one  outer  part.  Also,  where  the  natural  ten- 
dency of  a  note  is  disregarded,  the  effect  of  a  Hidden  Consecutive  is 
less  likely  to  be  agreeable  than  where  the  tendency  has  not  been  dis> 
turbed.  When  considering  the  introduction  of  a  Hidden  Consecutive, 
this  point  should  be  considered.  In  the  example,  the  downward 
tendency  of  F  (  the  4th  degree  of  the  scale  )  is  disregarded,  with  bad 
effect  where  the  neglect  is  made  prominent  by  being  in  the  Soprano. 
In  the  Alto  it  is  less  disagreeable,  though  it  is  easily  seen  that  the  effect 
of  such  progressions  might  be  made  still  better  by  observance  of  the 
Tendencies. 

Distribution  of  the  Parts. 

164.  ***To  produce  the  best  effect,  the  notes  of  a  chord  should  be 
at  about  an  equal  distance  from  each  other.  If  necessary  to  distribute 
them  unequally,  the  larger  intervals  should  be  in  the  lower  parts. 
Excepting  between  the  Bass  and  Tenor,  there  should  not  be  more 
than  an  octave  between  two  neighboring  parts.  Play  the  following  : 


Bad. 


Good. 


06  HARMONY  SIMPLIFIED. 

Opposition  of  Influences. 

165.  An  illustration  of  this  opposition  is  given  in  Fig.  48.  In  this 
ixample  there  is  a  tendency  on  the  part  of  the  Leading-note,  B,  to  as- 
»nd.  If  this  tendency  is  followed,  the  next  chord  will  have  no  5th. 


Fig.  48.< 


I 


As  in  some  cases  (  for  example  in  a  full  chorus  )  this  would  weaken 
the  effect  of  the  four  voices  singing  together  —  see  "  Influences  i  and 
8"  —  it  is  sometimes  better  to  sacrifice  the  upward  tendency  of  the 
Leading-note  in  order  to  gain  a  full  effect  in  the  following  chord, 
giving  the  progression : 


1 


In  disregarding  an  Influence  as  was  just  shown,  the  pupil  should 
guard  against  violating  some  other  Influence ;  for  example,  if  the 
Leading-note  were  in  the  Soprano  or  Bass,  it  could  not  progress 
downward  on  account  of  Influence  6.  The  effect  would  be  very  bad, 
as  shown  in  Fig.  46,  (a\ 

Again,  if  the  Bas?  note  G,  in  Fig.  48,  should  progress  downward 
to  C,  instead  of  upward,  the  leading-note  could  not  pass  downward,  on 
account  of  the  bad  Hidden  5ths  (  both  parts  moving  by  a  skip,  see 
§  »34);  e.g., 


166.    Another  illustration  of  the  manner  in  which  these  influences 
may  oppose  each  'Jther  is  shown  in  Fig.  49. 


HARMONY  SIMPLIFIED. 


97 


49. 


/ 


z      <^, 

H            II 

I?T\        rd 

^                            $j 

X3                     II 

v-LJ       g 

6?       2 

^ 

0      f* 
i    x 

J^T?               (*^ 

Bv          1 

J        B 

r                I 

-^         ^ 

1 

At  x  the  3rd  of  the  chord,  E,  is  doubled,  iu  opposition  to  Influ- 
ence 5.  The  reason  for  this  is  shown  in  Influence  2,  namely,  the 
advantage  of  a  smooth  progression  of  the  parts  :  also  in  Influence  4, 
for  if  the  Tenor  note,  E,  in  the  chord  marked  x,  be  changed  to  C  in 
order  to  avoid  doubling  the  3rd,  the  result  would  be  Consecutive  5ths 
with  the  Alto,  which  are  much  worse  than  a  doubled  3rd.  Contrary 
motion  and  the  Tendency  of  Continuity  combine  to  prevent  any  bad 
effect  which  might  be  expected  from  doubling  this  Tendency-note.* 

167.  One  more  illustration  may  be  given :  —  Influence  7  recom- 
mends the  retention  of  a  common  note  in  the  same  part  (  see  also 
§  102  ).  But  it  occasionally  happens,  that  other  considerations,  par« 
ticularly  Influences  2  and  8,  are  more  important,  and  demand  that  this 
Influence  be  sacrificed  for  them.  This  is  shown  in  Fig.  50.  Here 
the  note  C,  which  in  the  first  chord  is  taken  by  the  Tenor,  is  in  the 
second  chord  taken  by  the  Alto.** 


Fig.  SO. 


*  A  Melodic  Tendency  may  be  disregarded  far  more  freely  than  an  han 
ttionic  tendency,  since  the  former  can  be  removed  by  Continuity.  (See  §153.) 

**  If  circumstances  should  allow  the  rearrangement  of  the  first  chord,  it 
would  still  be  possible  to  retain  the  common  note  ;  e.  g., 


1 


This  would  illustrate  the  fact  that  in  writing  exercises,  if  the  pupil  finds  it  diffi- 
cult to  make  a  certain  connection,  by  going  back  a  few  chords  and  working  in  a 
different  position,  a  way  may  be  opened. 


p8  HARMONY  SIMPLIFIED. 

Many  other  illustrations  might  be  given,  showing  how  circum- 
stances alter  cases,  and  that  what  is  good  in  one  place  may  not  be 
best  in  another.  The  pupil  should  understand  that  part-writing  is  not 
a  question  of  following  rules,  but  is  a  matter  of  judgment,  controlled 
by  the  considerations  above  mentioned. 

In  general  the  pupil  will  find  that  .the  more  prominent  of  the 
above  Influences  are  Nos.  3, 4,  6,  and  7. 

General  Directions  for  Part-writing. 

1 68.  In  summing  up  the  above,  and  formulating  di- 
rections for  Part-leading  which  shall  be  simple  and  yet 
adapted  to  all  cases,  the  following  may  be  given : — 

(  i.)     Avoid  Consecutive  5ths*  and  8ves. 

(2.)  Avoid  Hidden  5ths  and  8ves  only  when  they 
make  a  bad  effect. 

(3.)  A  note  common  to  two  chords  is  to  be  retained 
in  the  same  part,  unless  some  other  Influence  requires 
another  progression. 

(4.)  Smooth  progressions  are  better  than  wide 
skips  in  the  parts. 

(5.)  Study  the  Influences.  If  they  agree,  there 
will  be  no  question  in  regard  to  the  progression.  If  they 
disagree,  let  the  stronger  rule  unless  consecutives  are  pro- 
duced. 

(6.)  Listen  to  the  effect.  If  it  is  bad  probably  some 
Influence  has  been  disregarded. 

(  7. )     Consider  the  range  of  the  voices.     (See  p.  60.) 
169.     From  this  time  forward,  the  teacher,   when  cor- 
recting exercises,   should  designate  which   Influence  has 


*  A  single  exception  may  be  given.     A  Perfect  sth  may  be  followed  by  a 

Dimin.  sth,  thus,  ES^^^:±Er|  but  not  reversed,  thus,  ^T^""""^"!], 

«/    Good.  ,/   Bad. 

because  the  latter  prevents  the  diminished  interval  from  contracting.  In  the 
opposite  direction,  the  tendency  to  contract  causes  a  return  to  the  first  har- 
mony (good).  See  footnote,  p.  49. 


HARMONY  SIMPLIFIED. 


99 


been  disregarded  in  each  case ;  or  he  may  simply  draw  'A 
line  through  the  wrong  note  and  mark  the  number  of  the 
influence  which,  if  followed,  will  rectify  the  error,  leaving 
the  pupil  to  change  it.  This  will  awaken  the  critical 
powers,  and  cultivate  the  judgment.  Also  allow  the 
pupils  to  correct  one  another's  work  according  to  the  same 
plan,  in  each  case  giving  the  reason  for  the  correction. 

NOTE.  The  pupil  should  distinguish  carefully  between  the  chord 
of  the  Dominant  seventh  on  G  and  the  chord  of  the  Dominant  seventh 
in  the  key  of  G.  The  former  has  the  note  G  for  its  root ;  while  the 
latter  is  built  upon  the  sth  degree  ( the  dominant )  of  the  scale  of  G, 
i.  e.,  D. 

Exercises. 

170.     Mark   the    Roman   Numerals  under  the  Basses 
before  proceeding. 

1.         J-367  6  4687 


-3=* 


2.       R'         5        ^ 67  4 


35 


;e 


.&. 


4. 


-z? h 


100 
5. 


HARMONY  SIMPLIFIED. 


7  57 

6.       J-       3          6          $  066,666  $~ 


B=P 


EHI 
^dil 


7.     J. 


^H 


5  7 
8.       J-  36*,  6         $  0         6          7          <  ~ 


9. 


7 
6          P 


v-fe-zt-  ^i^— ^z=l=^— ^-M2 — r4— ' 


8    7 

B  - 


10.    J- 


Exercises  fn  Harmonizing  the  Scale. 

171.  Harmonize  the  Major  and  Minor  scales,  using 
chords  of  the  7*h  where  possible,  and  the  triads  with 
inversions,  working  both  at  keyboard  and  in  writing. 

Synopsis. 
Write  the  usual  Synopsis  of  the  chapter. 


HARMONY  SIMPLIFIED.  ioi 


CHAPTER  VI. 

INVERSIONS    OF    THE    CHORD    OF    THE    SEVENTH. 

172.  We  have  repeatedly  seen  the  different  Positions 
of  the  Chord  of  the  Seventh.  We  will  now  consider  the 
Inversions,  which  are  very  similar  to  the  Inversions  oi 
Triads,  though  a  little  more  complicated,  owing  to  the 
presence  of  four  notes  in  the  chord.  Compare  the  fol- 
lowing with  §  125. 

(a.)   When  the  Root  is  in  the  Bass,  the  chord  is  in 
its  Direct  form. 

(6.)     When  the  Third  is  in  the  Bass,  the  chord  is  in 
its  1st  Inversion. 

(c.)     When  the  Fifth  is  in  the  Bass,  the  chord  is  in 
its  2d  Inversion. 

(d.)     When  the  Seventh  is  in  the  Bass,  the  chord  is 
in  its  yd  Inversion. 

The  Inversions  are  figured  and  named  as  follows : — 
Direct,  ist  Inversion.  2nd  Inversion.  3rd  Inversion. 
7  66  64  6 

5  or  7         5  or    5  4  or    3  4  or  2 

33  3  2 

Six-Five-Three,  Six-Four-Three,  Six-Four-Two, 

or  or  or 

Six-Five.  Four-Three.          Second. 


Example  :< 


V 

1                 i 

II 

1    ^           1    & 

S3Z    £? 

II 

«j      ^ 

o 

c~\  * 

(\        IT3 

|| 

*    1  • 

rt                       \ 

^ 

\ 

1 

^— 

•*^ 

1 

II 

7 

6        6 
S°r  5 

3 

64            6 
4  or  3            4  or  2 
3                    2 

,02  HARMONS   SIMPLIFIED. 

Exercises. 

(a.)  Taking  each  of  the  12  keys  in  turn,  write 
Chord  of  Dominant  Seventh  in  its  several  inversions,  and 
figure  them.  Vary  the  positions  in  the  different  exercises. 

(£.)      Repeat  the  above  at  the  keyboard,  in  all  keys. 

To  find  the  Root  of  a  Given  Chord  of  the  Seventh. 

Proceed  as  shown  in  §  129.  When  the  chord  is  in 
its  "  Direct  form,"  it  is  said  to  be  placed  in  3rds,  since 
each  note  is  a  3rd  above  the  one  next  below.  It  should 
be  noticed  that  when  placed  in  its  Direct  form,  a  chord  is 
always  figured  I,  or  such  part  of  these  figures  as  may  be 
necessary.  If  either  of  the  figures  2,  4,  or  6  appears,  an 
inversion,  and  not  the  direct  form,  is  present. 

Exercises. 

(a.)    Write  the  chords  indicated  by  the  following  fig- 
ured Basses,  and  mark  the  appropriate  Roman  numeral : 


(b.)  Play  the  chords  indicated  by  the  above  figured 
Basses. 

Resolutions  of  Inversions  of  the  Chord  of  the 
Dominant  Seventh. 

773.  If  the  simple  tendencies  shown  in  §  157  are  fol- 
lowed, the  pupil  will  have  no  difficulty  in  resolving  the 
inversions  of  the  Chord  of  the  Seventh.  Remember,  that 
the  Leading-note  tends  upward,  the  7th  from  the  root 
downward,  Augmented  intervals  tend  to  increase,  while 
Diminished  intervals  contract.  (  See  §§152  to  155.) 

Exercises. 

(a.)  Following  the  above  principles,  resolve  the 
inversions  shown  in  Fig.  51,  and  place  the  proper  Roman 
Numeral  under  each  chord. 


HARMONY  SIMPLIFIED. 


103 


Fig.  5  1 . 


(3.)  Write  inversions  of  the  chord  of  the  Dominant 
7th,  and  resolve  them,  in  the  keys  of  G :  F ;  D  ;  Bb ;  A ; 
Eb;  B;  Ab;  F». 

(r.)  Repeat  the  above  at  the  keyboard,  adding  all 
other  Major  and  Minor  keys. 

Exercises. 

1.         R'  66326  47 


T-l*     j 

j 

<5>       £* 

<-^ 

f3              m 

^      II 

~s  ffi  <&• 

2       (51 

0 

<=? 

2      R-      3        f        e        e        f 


i 


-& & 


R. 


Y^            —  ~ 

^2            '^ 

—       II 

~3L   n  *•  v 

P_ 

G 

II 

4. 


3636436 


&-3--=l 


8  7 
6         f- 


6.      R.                       0         f          6 

e 

6                    «    \ 
6                 4   f 

1  *^\"    I 

r"          '~~i 

— 

' 

rr?'(j> 

-        ?       *       c> 

—  1  ' 
-&  —  •*! 

- 

|        j 

i  :  1 

1  1  

—  i  —  jj^*  '^^-  —      '  —  *-* 

104 


HARMONY  SIMPLIFIED. 


7. 


e  7 
e        4  ft 


is; 


m 


8. 


6    7 

6         4    ft 


6  626  326 


£ 


4= 


6  87 

26  45- 


10.     J-        365 


266  36647 


3664 


t~ '  I  '         c^       &~     ^       C. 


11.  J. 


8  66  326 


P*F^ 

-ir— 

&-f= 

12.    J- 


HARMONY  SIMPLIFIED. 


105 


175.     Exercises  in  Harmonizing  the  Scale. 

Harmonize    the  scales,   using  the  chords  of  the  7th 
with  their  inversions,  and  the  triads  with  their  inversions. 


CHAPTER  VII. 

SECONDARY  CHORDS  OF  THE  SEVENTH. 

176.  The  chord  of  the  Dominant  Seventh,  because  it 
plays  such  an  important  part  in  the  key,  is  also  called  the 
Principal  chord  of  the  seventh.*  The  chords  formed 
upon  the  remaining  degrees  (for  they  are  nearly  all  found 
in  Harmony)  are  called  Secondary  or  Collateral 
Sevenths. 

Formation  of  Secondary  Chords  of  the  Seventh. 

As  seen  in  §§  147  and  148,  they  are  formed  by  the 
addition  of  a  7th  to  the  triads  upon  the  various  degrees 
of  the  scale.  As  the  triads  are  of  various  kinds,  viz., 
Major,  Minor,  Diminished  or  Augmented,  the  Secondary 
seventh-chords  will  have  the  same  variety  of  formation, 

*  It  is  also  called  the  Fundamental  Seventh,  since  its  intervals  are  formed 
like  those  of  Nature's  (Harmonic)  chord,  with  Major  triad  and  Minor  yth 
from  a  Root-tone.  (See  §  90.) 


I06  HARMONY  SIMPLIFIED. 

thus   contrasting   with   the   Dominant   Seventh   with    its 
Major  3rd  and  Minor  7th. 

This  irregularity  of  construction  should  not  be  considered  a  fault, 
for  the  chord  of  the  Dominant  7th  points  so  strongly  to  the  Tonic, 
that  if  all  the  Chords  of  the  Seventh  were  like  it  the  sense  of  Tonality 
would  be  disturbed.  (  See  §  266.)  As  it  is,  the  characteristics  of  the 
key  are  much  better  preserved  than  would  otherwise  be  the  case. 
Again,  as  we  need  Major,  Minor,  Diminished,  and  Augmented  triads 
to  make  up  the  complete  list  of  triads  in  a  key,  so  do  we  need  the 
same  variety  in  the  structure  of  the  Chords  of  the  Seventh. 

Resolution  of  Secondary  Chords  of  the  Seventh. 

177.  As  the  Secondary  Chords  of  the  7th  are  formed 
in  a  manner  similar  to  the  chord  of  the  Dominant  Seventh, 
so  their  resolution  follows  in  a  general  way  the  same  pat- 
tern; viz.,  the  Chord  as  a  whole  tends  to  resolve  to  the 
Triad  situated  a  4th  higher  than  the  root  of  the  Chord  of 
the  Seventh.  This  is  the  same  as  from  the  Dominant 
to  the  Tonic.  (See  §  158,  foot-note.)  More  accurately 
expressed,  the  chord  D-F-A-C  would  tend  to  resolve  to 
the  triad  on  G,  for  G  is  a  4th  higher  than  D.  So  also 
E-G-B-D  would  resolve  to  the  triad  on  A,  since  A  is  a 
4th  higher  than  E. 

The  individual  notes  in  a  Secondary  Seventh-chord 
have  a  tendency,  though  not  so  pronounced,  to  progress  as 
in  the  Dominant  Seventh-chord;  viz.,  the  7th  from  the 
root  may  descend,  and  the  3rd  from  the  root  may  ascend. 


Pig:.  52. 


1 


For  example,  in  Fig.  52  the  general  tendency  is  to  the 
triad  on  G  (the  Cadencing  Resolution ) .  The  7th,  C, 
being  a  minor  7th  and  therefore  a  dissonance  with  the 


HARMONY  SIMPLIFIED. 


I07 


a 

/L      ^ 

ff\\     t^> 

532     s 

t  A« 

~a.         II 

'1.          ^ 

^             ^^ 

M 

root,  tends  downward ;  F  tends  upward,  not  so  much  on 
account  of  any  dissonance  or  "  Influence,"  as  for  the  rea- 
son that  it  is  the  shortest  way  to  a  place  in  the  next  chord, 
and  that  we  are  accustomed,  in  the  chord  of  the  Domi- 
nant 7th,  to  hear  the  corresponding  tone  pass  upward. 
According  to  Influence  8,  it  could  also  pass  downward  to  D, 
making  the  second  chord  fuller.  For  many  cases  this  would 
be  better  than  the  upward  progression,  provided  that  it  made 
no  bad  hidden  5ths  with  the  Bass.  If  the  Bass  should  move 
upward  to  G,  this  would  be  quite  satisfactory ;  e.  g., 


53. 


Exercises. 

178.      (0.)     Form  Chords  of  the  7th  upon  all  degrees 
of  the  scale  of  C  Major,  and  resolve  them  as  shown  in  Fig. 

52>  or  53- 

NOTE.  The  resolution  of  the  seventh-chord  upon  the  4th  degree 
of  the  scale  to  the  triad  upon  the  7th  degree,  is  not  commonly  used,  for 
the  following  reason : —  A  Dependent  chord  demands  a  resolution 
to  an  Independent  chord.  Now,  as  the  triad  on  the  7th  degree  is  a  Di- 
minished triad,  it  is  not  Independent,  and  is  therefore  not  suited  to  be 
a  chord  of  resolution.  But  it  is  possible  to  use  this  progression  if 
the  triad  upon  the  7th  degree  should  in  its  turn  be  followed  by  an  in- 
dependent triad;  e.  g., 


Fig.  54. 


Another  restriction  in  the  use  of  the  chord  of  the  7th  on  the  fourth 
degree  of  the  scale  is  shown  in  the  foot-note'to  §  187. 

(6.)     Write   the    Secondary    Seventh-chords,   with 
resolutions,  in  the  keys  of  F,  G,  D,  Bb,  A,  El?  and  Fjf. 
(c.)      Repeat  the  above  at  the  keyboard. 


roS 


HARMONY  SIMPLIFIED. 


Chord  of  the  Seventh  upon  the  7th  Degree  in 

Major. 

179.     As  a  Secondary  chord  of  the  7th,  the  natural  res- 
olution of  this  chord  is  : 


VII07 

This  is  quite  correct.  But  a  more  common  resolu- 
tion is  found  in  a  consideration  of  the  following  • — 

We  have  seen  how  the  Leading-note  (7th  degree  of 
the  scale)  has  a  strong  tendency  to  progress  to  the  Tonic. 
(See  §  152.)  The  triad  formed  upon  this  note  has  also 
a  strong  tendency  to  progress  to  the  Tonic  triad  (  see 
Fig.  56) ,  resulting  from  this  tendency,  while  the  chord 
of  the  fth  upon  the  same  note  is  even  more  strongly  in- 
clined to  progress  in  the  same  direction.  E.g.,  (  plav 
it): 

(a.)  (6.) 


Fig.  56. 


1 


Triad.  Seventh. 

There  are  two  reasons  for  this  tendency;  viz., 

(a.)  The  tendency  of  the  Leading-note,  mentioned 
above. 

(3.)  The  similarity  of  construction  to  the  chord  of 
the  Dominant  Seventh,  which  progresses  naturally  to  the. 
Tonic.  For  example,  G-B-D— F  (play  it)  is  the  chord  of 
the  Dominant  7th,  resolving  to  the  Tonic  triad  C— E-G 
(play  it) .  If  now  the  Root,  G,  is  omitted,  we  have  the 
triad  B-D-F  remaining,  which  resolves  just  as  if  the  Root 


HARMONY  SIMPLIFIED. 


109 


were  present.  This  chord  without  the  root  (B-D-F) ,  is 
seen  to  be  the  same  as  the  triad  formed  upon  the  7th  de- 
gree of  the  scale.  Now,  as  the  triad  upon  the  7th  degree 
has  such  a  distinct  tendency  toward  the  Tonic  triad,  it 
will  be  readily  understood  that  the  chord  of  the  seventh 
upon  the  same  degree  has  a  similar  tendency,  which  is  in- 
creased, rather  than  diminished,  by  the  addition  of  the 
7th.  This  similarity  to  Dominant  harmony  will  be  further 
explained  in  Chapter  IX. 

1 80.  From  a  consideration  of  the  above,  it  will  be 
seen  that  the  Chord  of  the  Seventh  upon  the  7th  degree 
may  be  looked  upon  in  two  ways :    (  a  )      As  an  incom- 
plete   form  of    Dominant   harmony,    ( in  which    case  it 
would  resolve  most  naturally  to  the  Tonic  triad,  as  in 
Fig.  56,    b  )  ;  or  (  b  )   As  an  ordinary  Secondary   Sev- 
enth-chord upon  the  7th  degree,  resolving  most  naturally 
to  the  triad  a  4th  higher,  as  in  Fig.  55. 

Preparation  of  Dissonant  Intervals. 

181.  A  dissonance  may  be  either  agreeable  or  disa- 
greeable.    This  anomaly  is  explained  by  the  fact,   that 
although    a    chord    may    sound    well,    it    is   technically 
called  a  dissonance  if    it  demands  that  another  chord 
should  follow  to  give  a  feeling  of  completion  or  repose. 
(See  §§  150  and  151.)      It  was  formerly  the  rule,  that 
all  dissonances  should  be  "  prepared."      At  the  present 
day  it  is  the  custom  to  "prepare"    only    harsh    disso- 
nances.    The    chord  of  the  Dominant  seventh  was  the 
first  to  be  freed  from  the  restriction,  and  the  chord  of  the 
Diminished    seventh  is  also  free,*  while  the  Secondary 
Chords  of  the  Seventh,  and  the  Chord  of  the  Ninth  (par- 

*  Though  not  requiring  preparation,  it  is  well  to  approach  the  milder  disso- 
nances by  a  Diatonic  step  rather  than  by  a  skip. 


no 


HARMONY  SIMPLIFIED. 


ticularly  the  Minor  Ninth,  because  it  is  a  harsh  disso- 
nance) ,  are  usually  prepared.  "  Preparing  "  a  dissonance 
means,  that  the  note  which  causes  the  dissonance  shall  have 
been  present  as  a  consonance  in  the  chord  immediately 
preceding;  e.  g., 


The  note  C,  having  appeared  in  the  first  chord  as  a  con- 
sonant note,  is  thus  "  prepared  "  in  the  second  chord  where 
it  is  a  dissonant  note. 

182.  Instead  of  being  "  prepared,"  all  dissonant  notes 
may  enter  diatonically ;  i.  e.,  from  the  next  step  above 
or  below.  E.  g., 


(The  dissonant  note  C  enters  from  the  next  step  above.) 

In  general,  therefore,  we  should  not  skip  to  a  dissonant 
interval,  but  either  "  prepare"  it  or  lead  stepwise  into  it. 

183.  A  dissonant  note,  i.  e.,  a  note  which  forms  a 
dissonance  with  another,  should  not  be  doubled.  Being 
a  tendency-note,  as  all  dissonances  are,  if  it  were  to  be 
doubled  either  consecutive  Sves  would  result,  or  a  contra- 
diction of  its  natural  tendency  by  one  of  the  notes.  (  See 
§  162.) 


Exercises. 


2. 


R. 


HARMONY  SIMPLIFIED. 


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3. 


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m  &ARMONY  SIMPLIFIED. 

Succession  of  Chords  of  the  Seventh  ;  Resolu- 
tion of  one  Seventh-Chord  to  another  Seventh- 
Chord. 

185.  Instead  of  resolving  to  a  triad,  as  shown  in  the 
preceding  chapters,  a  Chord  of  the  Seventh  may  progress 
to  another  Seventh-Chord;  e.  g., 


Fig.  57  might  be  called  a  contraction  of   Fig.  58 ;  for, 


Fig.  58. 


since  the  Chord  of  the  Seventh  is  merely  an  enlarge- 
ment of  a  triad  (see  §  147  ),  we  are  allowed  to  progress 
directly  from  one  Seventh-Chord  to  another,  considering 
that  the  Tonic  Triad,  or  regular  resolution,  is  implied  in 
its  enlarged  form. 

Advanced  Course. 

See  "How  to  Modulate,"  page  42. 


HARMONY  SIMPLIFIED. 


3. 


IE 


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F 


Secondary  Sevenths  in  Minor. 

Advanced  Course. 

Exercises. 

187.  (  a.)  As  in  §  148,  the  pupil  will  form  Seventh- 
Chords  upon  each  degree  of  the  scale  of  C  Minor,  and 
describe  them. 

He  will  notice  that  some  of  these  Seventh-Chords, 
like  the  triads  of  the  Minor  scale,  are  too  harsh  for  practi- 
cal use,  owing  to  the  various  extremely  dissonant  intervals 
contained.  It  will  be  noticed  that,  beside  the  Dominant 
Seventh  (  'which  is  alike  in  Major  and  Minor  ) ,  the 
most  agreeable  of  the  Secondary  Chords  of  the  Seventh  in 
Minor  are  those  upon  the  2nd  and  7th  degrees.  The 
others,  either  on  account  of  their  harshness  or  the  forced 
leading  of  the  parts  in  their  resolution,  are  but  seldom 
used. 

(  6.)  The  pupil  should  try  to  resolve  the  Seventh- 
Chord  upon  each  degree  of  the  minor  scale  —  i.  e.,  the 
Cadencing  resolution  to  the  triad  a  4th  higher —  and  he 
will  see  the  difficulty  of  resolving  some  of  them  without 
bad  leading  of  the  parts.* 


*  The  pupil  will  find,  in  resolving  the  seventh-chord  upon  the  4th  degree, 
that  the  Bass,  if  moving  upv<ard  to  its  note  of  resolution,  passes  over  the  inter- 
val of  three  whole  steps,  an  awkward  skip  called  the  Tritone,  which  is  forbidden. 
It  may  progress  downward  to  the  octave  of  the  same  note  without  hindrance. 
Being  comparatively  ill  adapted  for  singing,  like  the  step  of  the  Augmented  2nd, 
!he  Tritone  is  not  to  be  used  for  the  present.  (  See  §  329^) 


HARMONY  SIMPLIFIED. 


1  88.  It  will  be  observed  that  the  chord  upon  the  7th 
degree,  though  a  very  agreeable  chord,  does  not  resolve 
well  to  the  Augmented  triad  a  4th  higher,  but  rather  in- 
clines to  the  triad  upon  the  ist  degree.  In  this  it  is  seen 
to  correspond  with  the  same  chord  in  Major,  i.  e.,  the 
Chord  of  the  Seventh  upon  the  7th  degree  (see  §  179  ), 
and  is  explained  in  the  same  manner,  viz.,  by  the  strong 
tendency,  of  the  7th  degree  of  the  scale,  or  Leading-note, 
toward  the  Tonic.  Fig.  59  illustrates  the  chord  of  the 
seventh  upon  the  7th  degree  in  minor,  with  the  resolution 
to  the  tonic  as  described  above.  The  interval  B-Ai?  is 
a  Diminished  7th,  and  from  this  interval  the  chord  is 
named  the  chord  of  the  Diminished  Seventh.  It  will 
be  further  explained  in  Chapter  IX. 


not  : 


Exercises. 


7          * 


626          0 


Inversions  of  Secondary  Chords  of  the  Seventh. 
Regular  Course. 

189.  In  §172  the  pupil  learned  to  form  Chords  of  the 
Seventh  upon  every  degree  of  the  scale,  also  to  invert 
and  figure  them. 


HARMONY  SIMPLIFIED. 


In  the  following  exercises,  containing  inversions  oi 
the  Secondary  Chords  of  the  Seventh,  no  new  points  are 
to  be  considered.  Attention  to  the  principles  of  Influ- 
ences and  Tendencies  will  guide  the  pupil  here  as  in  all 
other  chords. 

Exercises. 


II 


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U6  HARMONY  SIMPLIFIED. 

Cadences:  Closing  Formula. 

190.  It  has  been  remarked  that  the  succession  of  the 
Chord  of  the  Dominant  yth  and  the  Tonic  triad,  which 
gives  such  a  feeling  of  a  close,  is  called  a  Cadence,  or 
Cadencing  Resolution,  also  called  the  Authentic  Cadence. 

There  are  various  forms  of  ending  a  musical  thought, 
more  or  less  elaborate  and  of  varying  character  as 
regards  the  decisiveness  of  the  close.  In  ordinary  ca- 
dences the  Tonic  chord  occurs  upon  an  accented  part  of 
the  measure  (ttiesis),  and  the  Dominant  Seventh  on  an 
unaccented  part  (  arsis.  ) 

These  various  Cadences  are  named  and  defined  as 
follows : — 

Perfect  Cadence.  The  most  absolute  close  :  both  the 
Soprano  and  Bass  of  the  last  (  Tonic  )  triad  sound  the 
Root  of  the  chord.  (  Ex.  a,  Fig.  60.) 

Imperfect  Cadence.  Not  so  decisive  as  the  first :  either 
the  Soprano  or  Bass  does  not  sound  the  root  of  the  Tonic 
(  closing  )  triad.  (Ex.  £,  Fig.  60.) 

Plagal  Cadence.  Where  the  final  chord  is  preceded  by 
the  triad  on  the  Subdominant  instead  of  the  Dominant : 
an  old  church-form.  (  Ex.  c,  Fig.  60.) 

Half-Close.  Where  the  Dominant  follows  the  Tonic 
instead  of  preceding  it.  (  Ex.  d,  Fig.  60.) 

Deceptive  Cadence.  Where  the  Dominant  Seventh- 
chord,  instead  of  resolving  to  the  Tonic  triad,  progresses 
to  the  triad  on  some  other  degree  of  the  scale,  thus  disap- 
pointing and  deceiving  the  natural  expectation  that  it  will 
resolve  to  the  Tonic.  (Ex.  e,  Fig.  60.  See  §  192.) 

Modulatory  False  (  Deceptive  )  Cadence.  Where  the 
Dominant  Seventh-chord,  instead  of  resolving  to  the 
Tonic  triad,  progresses  to  a  chord  in  a  foreign  key,  thus 
producing  a  modulation.  This  will  be  further  explained 
in  §195.  (Ex./,  Fig.  60.) 


HARMONY  SIMPLIFIED. 
(a.)  (a.)          (c.)  (d.)         (f.)         (/.) 


Fig.  6O. 


Exercises. 

(<z.)  Return  to  the  exercises  in  §§  170,  173  and 
174,  and  describe  the  cadences. 

(3.)      At   the  keyboard,  form  examples  of  each  of 
the  different  Cadences,  using  many  different  keys. 
Closing  Formula. 

191.  A  more  extended   form  of  close,  which  includes 
the   Cadencing  resolution    shown    above,   is   called  the 
Closing  Formula.     It  will  be  seen  that  not  only  does  the 
chord  of  the  Dominant  7th  point  directly  to  the  close, 
but  that  there  is  a  distinct  impression  in  the  preceding 
chords.     Many  changes  can  be  made  in  the  succession  of 
chords  constituting  the  Closing  Formula,  there  being  no 
rule  as  to  their  order.     A  few  of  the  more  common  forms 
are  — («.)   IV,  V7  I.     (3.)   IV,  It  V7,  I.     (c.)  n,  V7, 
I.    (</.)  IV,  n,  V7,  I.     Play  them. 

The  Closing  Formula  is  useful  in  giving  a  sense  of 
close  at  the  end  of  a  phrase,  or  in  establishing  a  key  after 
a  modulation.  (See  §  289.) 

Keyboard  Exercises. 

IMPORTANT  NOTE.  The  Closing  Formula  should  be.  made  the 
basis  of  an  extended  course  of  Keyboard  Exercises,  in  connection  with 
the  following  chapters,  including  all  the  Major  and  Minor  keys. 

Non-Cadencing  Resolutions  of  the  Chord  of  the 
Seventh. 

192.  The  resolution  of  the  Dominant  seventh-chord  to 
the  Tonic  triad  has  been  shown  as  the  most  natural  pro- 
gression.    There  are  many  other  resolutions  possible, 


n8  nAKMONY  SIMPLIFIED. 

which  are  called  non-cadencing  resolutions,  for  the  rea- 
son that  the  Chord  of  the  Seventh  does  not  move  in  the 
manner  of  a  Cadencing  Resolution  to  the  triad  a  4th 
higher  (  i.  e.,  the  Tonic  triad),  but  progresses  to  the 
triad  upon  some  other  degree  of  the  scale,  or  even  to  a 
chord  in  another  key.  Non-cadencing  resolutions  are 
useful  in  composition  when  it  is  desired  to  employ  the 
chord  of  the  Dominant  yth  and  still  avoid  a  close  which 
is  so  plainly  indicated  by  the  use  of  the  Dominant  7th 
followed  by  the  Tonic  triad. 

Among  these  Non-cadencing  resolutions  are  the 
Deceptive  Cadence  and  the  Modulatory  False  Cadence, 
both  of  which  are  classed  among  the  cadences  (§  190  )  by 
name  only,  not  being  true  Cadences. 

In  Non-cadencing  resolutions  the  Tendencies  and 
Influences  are  in  a  somewhat  greater  degree  disregarded, 
the  progressions  consequently  being  usually  rather  un- 
natural, and  in  some  cases  quite  forced.  But  if  we  were 
to  use  only  the  simplest  and  most  natural  progressions, 
the  variety  of  effects  would  be  very  limited.  It  will  be 
observed  that  in  the  Non-cadencing  resolutions  the  disso- 
nant intervals  do  not  always  resolve  to  the  nearest  conso- 


193.  As  the  pupil,  after  studying  the  use  of  the  common  note  in  con- 
necting two  triads  (  102 ),  at  once  learned  how  to  connect  two  triads 
without  that  common  note,  thus  enlarging  his^  powers,  so  here,  after 
learning  the  natural  resolution  of  the  chord  of  the  7th,  the  pupil  finds 
enlarged  possibilities  in  the  management  of  these  chords  by  the  use 
of  the  Non-cadencing  resolutions.  They  should  be  understood  not  as 
contradictions,  but  as  enlarged  liberties  in  the  treatment  of  the  Chord 
of  the  Seventh,  for  instead  of  forcing  the  Chord  of  the  Seventh 
always  to  resolve  to  the  Tonic,  it  is  allowed,  so  to  speak,  to 
mingle  with  a  larger  circle,  or  to  progress  to  triads'  upon  other 
degrees  of  the  scale,  or  in  other  keys.  This  gives  it  a  freedom 
similar  to  that  of  the  triads,  which  are  at  liberty  to  progress  not  only  to 
other  triads  having  a  common  note,  but  also  to  nearly  all  others  which 


HARMONY  SIMPLIFIED. 


can  be  reached  without  bad  leading  of  the  parts.  Many  of  these  pro- 
gressions should  not  be  called  resolutions,  since  the  Tendencies  and 
Influences  are  disregarded,  but  should  rather  be  called  connections, 
being  connected  with  the  following  chord  in  the  same  manner  as  the 
triads.  Indeed,  it  should  not  be  forgotten  that  Chords  of  the  7th  are 
merely  Triads  with  one  or  more  notes  added,  and  therefore  they  may 
easily  be  expected  to  retain  the  properties  and  privileges  of  triads. 

Exercises. 

194.  Below  are  given  examples  of  Non-cadencing  res- 
olutions and  connections.  Analyze  them,  pointing  out 
the  unnatural  progressions  of  the  dissonant  intervals,  and, 
if  possible,  giving  the  reason.  It  will  be  noticed  that  the 
7th  is  frequently  stationary,  or  even  progresses  upward, 
thus  giving  the  effect  of  a  connection  or  progression  from 
chord  to  chord,  rather  than  the  resolution  of  a  dissonance. 
When  the  Tendencies  and  Influences  are  disregarded, 
especial  care  must  be  taken  not  to  violate  the  rules  of 
correct  part-leading. 

N.  B.  N.  B. 


Fig.  61. 


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N.  B. 


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The  possible  combinations  with  the  Non-cadencing 
resolutions  of  the  Chords  of  the  Seventh  are  almost  lim- 


I20  HARMONY  SIMPLIFIED. 

itless,  as  will  be  shown  in  the  next  exercises.  The  above 
examples  marked  N.  B.  show  the  connection  of  the  Dom- 
inant seventh-chord  with  the  Dominant  seventh-chords  of 
various  foreign  keys:  such  connections  will  be  further 
explained  in  the  chapter  on  Modulation. 

Keyboard  Exercises. 

Advanced  Course. 

195.     Non-cadencing  Connections  with  Triads 
in  the  Key. 

(a.)  Starting  upon  the  Chord  of  the  Dominant  7th  in  the  key  of 
C,  try  to  resolve  it  to  (  or  connect  with  )  the  triad  upon  each  degree  of 
the  key  of  C.  If  the  effect  is  not  good,  try  a  change  of  position  in  the 
first  chord:  if  the  different  leading  of  the  parts  does  not  produce  an 
agreeable  effect,  reject  the  triad  and  try  the  next  one. 

(  b.)     Repeat  in  various  keys. 

Non-cadencing  Connections  with  Triads  Foreign 
to  the  Key. 

( c.)  Starting  upon  the  Chord  of  the  Dominant  7th  in  the  key  of 
C,  try  to  connect  it  with  the  Major  triad  upon  each  degree  of  the 
Chromatic  scale.  Reject  the  unsatisfactory  progressions. 

( d.)  Try  to  connect  the  Chord  of  the  Dominant  7th  in  C  with 
the  Minor  triad  upon  each  degree  of  the  Chromatic  scale,  as  above. 

( e.)  Starting  upon  the  Dominant  Seventh-Chord  in  other  keys, 
try  to  connect  with  the  Major  and  Minor  triads  as  before,  rejecting  all 
progressions  that  cannot  be  made  effective. 

Non-cadencing  Connections  with  Dominant 
Seventh-Chords  in  Foreign  Keys. 

(f.)  Starting  upon  the  chord  of  the  Dominant  7th  in  C,  try  to 
connect  it  with  the  chord  of  the  Dominant  7th  in  all  other  keys  (  pro- 
ceeding Chromatically  as  before). 

(g.)  Starting  upon  the  chord  of  the  Dominant  7th  in  other  keys, 
try  to  connect  with  all  other  chords  of  the  Dominant  7th  as  above. 

In  the  above  exercises  it  will  be  found  that  those  connections  are 
best  which  have  a  note  common  to  both  chords,  and  that  few  con- 
nections can  be  made  without  it. 

The  exercises  at  (/)  and  (g)  will  be  treated  further  in  Chapter 
XIII. 


HARMONY  SIMPLIFIED. 


121 


Ig6.  Exercises. 

1.         R'    3  76  587  677 


-p=__i_(S,__^=c===pi=^ 


2.        R.      5  6 


7  2667 


647  2 


5655  765  66  7 


Open  Position. 


5. 


6. 


6    7 

4    $  6, 


^ 

n    (gi- 


i 


7. 


6    I  6 

4*60  6          ,5 


ii 


8.       R.      5 


7 .         6  4  7 


133  HARMONY  SIMPLIFIED. 

Non-Cadencing  Connections  of  Secondary 
Chords  of  the  Seventh. 

197.  We  have  seen  how  the  Chords  of  the   Domi- 
nant  Seventh   are    frequently    connected    with    chords 
other  than  those  forming  the  Cadencing  resolution. 

The  Secondary  Chords  of  the  Seventh  are  capable 
of  being  treated  in  a  similar  manner.  Many  of  them, 
especially  in  Minor,  which  cannot  be  used  in  the  Ca- 
dencing resolution,  may  be  connected  with  other  chords 
with  very  good  effect.  As  in  the  free  resolution  of  the 
Dominant  Seventh-chord,  the  yth  from  the  root  may  pro- 
gress downward,  remain  stationary,  or  progress  upward, 
as  desired. 

Keyboard  Exercises. 

198.  (  a.)     Try  in  succession  the  Secondary  Seventh- 
Chords  in  the  key  of  C  major,  and  find  as  many  agreea- 
ble connections  with  other  chords  as  possible  (  even  con- 
necting with  chords  in  other  keys  ) ,  proceeding  in  detail 
as  shown  in  §  195. 

(<$.)  Proceed  similarly  with  the  Secondary  Seventh- 
Chords  in  C  minor ;  also  in  other  keys. 

Rules  for  Figured  Bass. 

199.  Short  horizontal  lines  following  figures  denote 
the  retention  in  the  following  chord,  or  continuation,  of 
the  notes  indicated  by  the  figures.     E.  g.,  the  notes  in- 
dicated by  6  and  by  3  are   continued   into  the  following 
chord.     In  notes,  thus  : — 


HARMONY  SIMPLIFIED. 


Even  when  the  Bass  note  changes,  the  horizontal 
lines  denote  the  continuance  of  the  notes  already  sound- 
ing, whether  indicated  by  figures  in  the  preceding  chord 
or  not ;  e.  g., 


200. 


Exercises. 


766 
76          564        5 


1 


'-i 
E 


23Z 


4. 


66  66 

&,  54        777       6 |_6_X2      •L_l_7_ 


6.     J- 


e.    J. 


b     6 


6 

5       J- 


HARMONY 


8.      J- 


6  7  5 


22: 


7b       8[J 


9.      J. 


70  I 


m 


7t>      etj  eQ 


8    7 
S    - 


1 


s^~ -"g 1 


-&- 


t^- 


Analytical  and  Comparative  Review. 
201.  The  pupil  should  strive  to  keep  his  knowledge 
collected  and  classified.  To  this  end  it  is  desirable  to 
tabulate  some  of  the  facts  already  learned,  the  student 
being  expected  to  find  the  definitions  and  commit  them 
to  memory  if  he  is  not  already  familiar  with  them. 

(i.)     Hoiv  the  terms  Major,  Minor,   Augmented, 
and  Diminished  are  used. 
I.     Intervals:  —        -, 

there  are  —   'Major,  Minor,  Augmented, 
II.     Triads  :  —  j  Diminished. 

there  are  —    J 
III.     Chords  of  the  ) 

Seventh:  —  (.Major,   Minor,    Dimin- 

the  ;th  may  be—  )  ished. 


HARMONY  SIMPLIFIED.  235 

(2.)      How  the  term  Principal  is  used: — 
I.     Triads  :  —  Tonic,   subdominant,  and  Dominant 
II.     Chords  of  the  Seventh  :  —  Dominant. 
(3-)      How  the  term  Secondary  is  used: — 

I.  Triads :  —  Upon    all  degrees  not  occupied   by 
Principal  triads. 

II.  Chords  of  the  Seventh  : —  Upon  all  degrees  not 
occupied  by  Principal  Seventh. 

(4-)      Of  Tendencies : — 

I.   Of  Leading-note  —  to  the  Tonic. 
II.  Of  the  Third  —  upward. 
III.   Of  the  Fourth  —  downward. 
Melodic :—     -j  IV.  Of    Continuity  —  to    continue     in 

either  direction. 

V.  Of  an  accidental  Sharp  — to  ascend. 
L  VI.  Of  an  accidental  Flat  —  to  descend. 

I.  Of   a  Diminished  Interval ; —  to  be- 

,,  come  still  less. 

Harmonic: — -!    TT     „,         .  ._ 

11.   Of  an  Augmented  Interval ; —  to  be- 
come still  greater. 

(  5«)      Natural  Resolutions : — 

I.     Of  Dominant  Seventh ; —  to  triad  a  4th  higher, 
i.  e.,  the  Tonic. 

II.  Of  Secondary  Sevenths ; — to  triad  a  4th  higher. 

III.  Of  Seventh-Chord  on  yth  degree ; —  to  Tonic 
or  to  triad  a  4th  higher. 

(  6.)      Non-  Cadencing  Resolutions : — 

I.     Of  Dominant  Seventh  ; —  to  secondary  triads 
in  the  key. 

II.     Of  Dominant  Seventh  ; — to  foreign  chords. 

III.  Of  Secondary   Sevenths; — to    various   triads 
in  the  key. 

IV.  Of  Secondary  Sevenths ; —  to  foreign  chords. 


«26  HARMONY  SIMPLIFIED. 

(7.)      Figuring  Inversions: — 
I.     Of  Triads ;  — •  According  to  distance  from  actual 
Bass. 

II.     Of  Chords  of  the  Seventh ; —  Same  as  triads. 

Synopsis. 
Write  the  usual  Synopsis  of  the  chapter. 

Historical. 
Concluded  from  page  39. 

Triads  and  Chords  of  the  Seventh. 

202.  With  Palestrina  (early  in  the  i6th  century)  the 
Harmonic  effects  began,  though  unconsciously,  to  appear 
upon  the  horizon  of  musical  development.  First  the 
Common  chord  was  used  in  its  direct  form,  then  with  its 
inversions.  Next  we  find  the  alternation  of  consonances 
and  dissonances,  and  after  a  time  Suspensions  and  Reso- 
lutions. The  use  of  the  Chord  of  the  Seventh  (  Domi- 
nant seventh  )  met  with  much  opposition  at  first.  For 
many  years  its  dissonant  notes  were  "  prepared,"  but  in 
recent  times  gradually  increasing  freedom  has  been  al- 
lowed, until  now  the  chord  can  be  used  without  especial 
caution.  Following  in  the  path  of  the  Chord  of  the 
Seventh  came  the  Chords  of  the  Ninth,  the  Chord  of  the 
Diminished  Seventh,  and  the  chords  of  the  Augmented 
Sixth  (  to  be  described  in  subsequent  chapters  ) ,  all  of 
which  have  been  shown  to  be  various  forms  of  Dominant 
(  or  Dependent  )  harmony.  Afterward  came  the  various 
forms  of  ornaments,  and  devices  for  imparting  variety, 
shown  in  Part  III. 

The  development  of  the  Harmonic  System,  and  of 
the  modern  scale  as  opposed  to  the  Gregorian  Modes, 
were  to  a  great  extent  coincident  and  mutually  dependent ; 
for,  whereas  the  Gregorian  Modes  were  formed  in  refer. 


HARMONY  SIMPLIFIED. 


127 


ence  to  the  Melody,  the  modern  scale  was  designed  with 
direct  reference  to  the  requirements  of  chord-construction. 
(  See  §  46.  ) 

This  brings  the  history  to  the  close  of  the  i6th  cen- 
tury, when  it  was  substantially  as  it  is  to-day.  The 
boundaries  of  the  keys  had  been  well  defined,  and  the  use 
of  the  more  ordinary  chords  had  become  common. 
Since  then  more  freedom  in  the  use  of  the  Dependent 
chords  has  been  gained,  and  a  knowledge  of  those  closely 
related  chords  which  lie  just  beyond  the  limits  of  a  key, 
but  are  used  as  if  they  belonged  to  it.  (  See  Chap.  XII.) 
During  the  last  two  centuries  progress  has  been  more  ir 
the  line  of  development  than  of  discovery. 
(  End  of  Historical  Remarks.) 

The  Perceptive  Faculties. 

203.  The  teacher  will  not  need  further  detailed  instructions,  as 
the  same  manner  of  hearing  the  tones  individually,  of  singing  them 
by  syllable,  of  writing  them,  and  hearing  them  collectively,  is  here 
followed.  The  teacher  should  be  careful  to  grade  his  instruction 
in  this  department  well  within  the  abilities  of  the  pupil,  and  to  pro- 
ceed very  slowly.  Exercises  in  Rhythm,  and  in  Altered  intervals 
( Aug.  and  Dim.),  may  properly  be  introduced  or  continued  at 
this  period. 


CHAPTER  VIII. 

THE    CHORD    OF   THE    DOMINANT    SEVENTH    AND  NINTH. 

204.  The  formation  of  chords  has  been  repeatedly 
shown  to  be  a  process  of  building,  or  adding  to  a  Rootoi 
Fundamental  note.  (See  §§90  and  147.)  It  has  alsc 


128  HARMONY  SIMPLIFIED. 

been  noticed  that  each  note  added  is  at  the  interval  of  a 
3rd  from  the  next  lower  note. 

If,  according  to  this  plan,  a  note  be  added  to  the 
Chord  of  the  Seventh,  there  will  be  produced  a  chord  of 
the  Seventh  and  Ninth,  called  also  the  chord  of  the  Ninth. 
As  the  one  most  commonly  used  is  derived  from  the 
Dominant,  we  will  consider  only  that  one  at  present. 
In  Fig.  62  is  shown,  at  (0),  the  chord  of  the  Seventh, 
and  at  (  b  )  the  same  with  the  9th  added. 
(«0 


In  a  Major  key  the  9th  will  be  Major;  and  in  a 
Minor  key  the  9th  will  be  Minor,  as  shown  in  Fig.  63 ; 
the  9th,  A,  being  made  flat  by  the  signature. 


Fig.  63. 

The  pupil  should  not  look  upon  this  as  a  new  and 
strange  chord,  but  as  a  Chord  of  the  Dominant  Seventh 
with  an  interval  added.  The  Chord  of  the  Seventh  was 
produced  by  adding  a  note  to  the  triad,  and  the  Chord  of 
the  Ninth  is  formed  by  a  further  addition  of  a  note  to  the 
chord  of  the  Seventh. 

205.  The  characteristics  of  the  chord  ( the  dissonant 
intervals  and  the  Tendencies  )  are  not  changed  by  add- 
ing the  new  interval,  as  may  be  seen  by  tracing  the 
dissonant  intervals  in  the  same  manner  as  shown  in 
§  157.  It  is  apparent  that  the  added  note  merely  creates 
two  new  dissonant  intervals,  the  9th  from  the  root,  and 
the  7th  from  B.*  As  both  these  intervals  would  be  re- 

*  In  the  chord  of  the  Minor  Ninth  there  is  also  the  dissonant  interval  of  a 
Diminished  sth,  D-Ab,  in  Fig.  63. 


HARMONY  SIMPLIFIED. 


129 


solved  by  allowing  the  pth,  A,  to  descend  in  the  resolu- 
tion of  the  chord,  it. is  apparent  that  the  addition  of  the 
new  interval  does  not  alter  the  natural  resolution  of  the 
underlying  chord  of  the  fth,  or  in  any  way  change  its 
nature.  We  merely  need  to  be  careful  to  avoid  consecu- 
tive 5ths,  which  may  occur  in  adding  the  new  note.  The 
Tendencies  of  the  various  notes  and-  intervals  are  not 
changed.  Therefore,  the  chord  of  the  Dominant  Seventh 
and  Ninth  is  seen  to  be  only  an  enlarged  form  of  Dom- 
inant Harmony. 

206.  Fig.  64  illustrates  the  resolution  of  the  chord  of 
the  Dominant  seventh  and  ninth  according  to  the  above, 
the  first  chord  being  used  to  prepare  the  dissonance  (  see 
§  181  ),  which  is  particularly  harsh  when  entering 
abruptly.  As  there  are  Jive  notes  in  this  chord,  one  must 
be  omitted  in  four-part  writing.  The  5th,  being  the 
least  essential  and  characteristic,  and  also  the  tone  with 
which  the  ninth  might  create  consecutive  5ths,  is  usually 
the  one  left  out. 

Major.  Minor. 


Fig.  64. 


mi 


, i i 


* 


1 


E 


Keyboard  and  Written  Exercises. 

207.  From  the  chord  of  the  Dominant  Seventh  in 
every  key,  both  Major  and  Minor,  form  the  chord  of  the 
Seventh  and  Ninth;  find  and  describe  their  dissonances 
and  Tendencies  as  shown  in  §  157;  prepare  and  resolve 
them  as  shown  in  Fig.  64. 

The  consideration  of  the  above  is  of  great  importance  and 
should  be  thoroughly  understood,  as  the  following  chapters  are  de- 
rived directly  from  this  section. 


,30  HARMONY  SIMPLIFIED. 

Inversions  and  Figuring. 

208.  The  inversions  of  this  chord  are  used,  excepting 
those  in  which  the  root  and  the  9th  come  too  close  to- 
gether.    The  figuring  is  similar  to  that  of  the  Chords  of 
the  Seventh,  the  added  note  simply  adding  a  figure. 

Exercises. 
Form    examples  of  inversions  of  the  Chord  of  the 

seventh  and  ninth. 

Secondary  Chords  of  the  Seventh  and  Ninth. 

209.  Secondary  chords  of  the  Seventh  and  Ninth  are 
occasionally  used,  though  not  often.     Not  belonging  to 
Dominant  harmony,  the  9th  and  the  7th  ( the    dissonant 
intervals)    must   both  be  prepared.     In  the   Dominant 
Seventh  and  Ninth-Chord  the  preparation  is  not  obliga- 
tory, though  customary. 

Synopsis. 
Write  the  usual  synopsis  of  the  chapter. 


CHAPTER   IX. 

THE   CHORD   OF   THE   DIMINISHED   SEVENTH. 

210.  The  Diminished  Triad  and  Chord  of  the  Seventh 
upon  the  7th  degree  in  Major  have  already  been  mentioned 
as  partaking  of  the  qualities  of  Dominant  harmony  (§179). 
The  Chord  of  the  Seventh  upon  the  7th  degree  in  Minor 
partakes  of  these  qualities  even  more  strongly.  (See  §  188.) 
They  are  both  considered  as  incomplete  forms  of  Dominant 
harmony.  The  one  formed  upon  the  7th  degree  in  Minor 
is  especially  important,  as  it  occurs  very  frequently,  gives 
a  smooth  effect  without  being  prepared,  and  is  of  great 
value  in  modulations.  (See  §  300.) 


HARMONY  SIMPLIFIED. 


Construction   of    the   Chord  of    the    Diminished 
Seventh. 

2ii.  This  chord  is  derived  from  the  Chord  of  the 
Dominant  Seventh  and  Ninth  in  the  Minor  mode,  by 
simply  omitting  the  root. 

(a.)          <*.) 

Fig.  65.  '     "    ' 

In  Fig.  65  at  (  a  )  is  given  the  Chord  of  the  Domi- 
nant 7th  and  9th  as  shown  in  Fig.  63.  If  the  root  is 
omitted,  we  have  the  chord  shown  at  (  b  ),  Fig  65,  which 
is  a  chord  of  the  Diminished  Seventh,  but  it  is  consid- 
ered as  derived  from  the  root  G  (indicated  in  Fig.  65 
by  W  ) »  and  therefore  having  the  same  resolution  as  if 
the  root  were  actually  present.  Therefore  we  say  that 
the  chord  of  the  Diminished  Seventh  is  an  incomplete 
form  of  Dominant  harmony. 

In  the  chord  of  the  Dominant  7th  and  9th  the  disso- 
nant intervals  are  the  Minor  7th  from  the  root  and  the 
Minor  9th.  In  the  chord  of  the  Diminished  Seventh, 
the  same  notes,  F  and  At?,  form  the  dissonances, 
appearing  as  a  Diminished  5th  and  a  Diminished  7th 
from  the  Bass  of  the  chord.  These  dissonances  are  re- 
solved in  the  same  manner  as  if  the  root  were  also 
sounding,  e.  g., 

± 


Fig.  66. 


-fr ^ 


-~^& 


|] 


i 


NOTE.  The  same  rules  for  doubling  notes  apply  here  as  in  the  simple 
Dominant  form ;  i.e.,  do  not  double  the  real  jd  and  ;th,  even  though  they 
appear  to  be  the  root  and  5th  (§  157). 


132  HARMONY  SIMPLIFIED. 

Keyboard  and  Written  Exercises. 

212.  (  i  )  Form  Chords  of  the  Minor  7th  and  9th 
upon  all  notes  from  C  to  C,  i.  e.,  upon  C,  Cj,  D,  Djf, 
etc ;  also  using  flats  instead  of  sharps,  as  Di?  for  Cj,  EP 
for  D$,  etc. 

(  2  )  From  each  chord  of  the  Minor  9th  just 
written,  form  a  chord  of  the  Diminished  7th  by  omitting 
the  root  and  writing  the  sign  W  in  its  place. 

( 3  )  Resolve  each  chord  of  the  Diminished  7th 
according  to  the  tendencies  in  §  157.  N.  B.  It  will  be 
found  that  the  resolution  is  the  same  as  if  the  root  were 
still  sounding;  see  Fig.  64. 

Use  of  the  Chord  of  the  Diminished  Seventh  in 
Major  Keys. 

213.  In  §  204  it  was  apparent  that  the  Chord  of  the  gth 
is  Major  in  Major  keys,  and  Minor  in  Minor  keys.     The 
Chord  of  the  Minor  9th  and  its  derivative,  the  Chord  of 
the  Diminished  7th,  are,  however,  often  used  in  Major 
keys;  the  9th  from  the  root  being  lowered  by  an  acci- 
dental ;  e.  g., 


Flg.  67. 


As  the  Chord  of  the  Dominant  Seventh  is  alike  in 
Major  and  Minor,  we  may  say  that  it  resolves  equally 
well  to  Major  or  Minor  triads ;  and  the  same  holds  good 
of  all  forms  of  Dominant  harmony,  whether  Chords  of 
the  7th,  of  the  7th  and  9th,  or  of  the  Diminished  7th. 

Keyboard  and  Written  Exercises. 

214.     (  i  )     From  the  Chord  of  the  Dominant  7th,  in 
all  major  keys,  form  Chords  of  the  Major  9th  as  shown 


HARMONY  SIMPLIFIED.  133 

in  Fig.  62.  From  these  chords  of  the  Major  pth  form 
chords  of  the  Minor  9th  by  lowering  the  Ninth  by  an 
accidental.  Omit  the  root  of  the  Minor  ninth-chords, 
producing  Chords  of  the  Diminished  7th  in  Major. 

(  2  )  Resolve  these  chords  of  the  Diminished  7th 
as  in  Fig.  66  or  67.  N.  B.  The  chord  of  the  Dimin- 
ished 7th  resolves  to  either  a  Major  or  a  Minor  triad,  as 
mentioned  in  §  213. 

Similarity  of  Sound  of  the  Diminished  Seventh- 
Chords. 

215*  Write  the  chords  of  the  Diminished  Seventh  as 
in  Fig.  68.*  Now  play  them  upon  the  piano,  and  it 
will  be  seen  that  there  are  apparently  but  three  differ- 
ent chords,  if  we  consider  that  inverting  and  changing 
the  notation  do  not  alter  the  sound.  This  is  shown  in 
Fig.  68»  where  the  chords  are  divided  into  four  groups, 
w,  #,  _y,  z ;  and,  by  trying  at  the  Piano,  it  will  be  seen 
that  No.  I  of  group  iv  is  the  same  as  No.  i  of  group  x, 
or  y,  or  z,  in  that  the  same  notes  are  struck  on  the  key- 
board. The  difference  consists  in  the  fact  that  the  chord 
is  inverted  and  differently  written.  Therefore,  any  chord 
of  the  Diminished  Seventh  can,  by  changing  its  nota- 
tion, belong  to  four  different  keys.  This  subject  will  be 
explained  further  in  §  300. 

(«>)  (*)  (y)  (*) 


Fig.  68. 


Roots :  (  G   I  GS   t  A    I  AS  (  B  I  C  J  CS  j  D  (  Df  (  E  (  F  j  F« 
Keys  :    }  C   \  C$  }  D    }  DS  \  E  }  F  \  FJf  \  G  \  GS  \  A  \  &  \  B 


*  The  pupil  should  write  a  series  (Chromatic)  to  represent  the  roots  of  the 
chords,  as  shown  in  the  line  marked  "Roots  "in  Fig.  68  and  try  to  build  the 
required  chords  from  these  roots  (as  shown  in  §  212)  without  referring  to  Fig. 
68  unless  necessary. 


,34.  HARMONY  SIMPLIFIED. 

The  chord  of  the  Diminished  7th,  being  Dominant 
harmony,  does  not  require  preparation. 

Inversions  and  Figuring. 

216.  The  chord  of  the  Diminished  yth  is  used  in  all 
inversions,  which  are  figured  by  counting  from  the  actual 
Bass  note,  as  for  other  chords.     The  sign  °  is  used  to 
indicate  Diminished. 

Exercises. 

(  a.)  Form  a  series  of  Diminished  seventh-chords 
similar  to  that  shown  in  Fig.  68,  but  with  the  sharps 
changed  to  flats;  e.  g.,  instead  of  using  FJ  for  the  Root 
of  a  chord,  write  it  GP,  which  will  cause  the  whole 
chord  to  appear  without  sharps.  Divide  the  series  into 
groups  as  shown  in  Fig.  68,  and  number  them.  Write 
also  the  Roots  and  Keys  under  the  chords  as  there  shown. 

217.  It  will  now  be  observed,  that  by  changing  the 
notation  of  the  Root  (  i.  e.,  from  a  sharp  to  a  flat,  or  vice 
versa  ) ,  the  notation  of  the  whole  chord  is  changed,  al- 
though the  notes  on  the  keyboard  remain  the  same. 

218.  It  will  also  be  seen, —  the  first  chord  of  each 
group  (  see  Fig.  68  )  being  the  same, —  that,  by  a  change 
of  Root  (and  therefore  of  notation),  the  same  chord  (  i.  e., 
upon  the  keyboard  )  may  become  Dominant  harmony  in 
four  different  keys,  as  shown  by  the   series  of  keys  in 
Fig.   68.     As  Dominant  harmony  resolves  naturally  to 
its  Tonic,  it  is  clear  that  by  proper  notation  these  chords 
of  the  Diminished  seventh  can  resolve  to  any  one  of  four 
different  keys. 

Exercises. 

219.  (<5.)      Completing  Fig.   68  as  required   in  the 
foot-note,  §  215,  take  the  first  chord  of  each  group  in 
Fig.  68,  and  resolve  it  to  its  proper  Tonic  triad  as  indi- 
cated by  the  notation. 


HARMONY  SIMPLIFIED. 


J35 


(  c.)  Take  the  second  chord  of  each  group,  and  pro- 
ceed as  before. 

(  d.)  Take  the  third  chord  of  each  group,  and  pro- 
ceed as  before. 

(e.)  Name  the  Root  of  the  Diminished  seventh- 
chord  which  shall  resolve  to  the  triad  of  D  major. 
(  N.  B.  The  Root  of  the  chord  is  desired,  not  the  Bass 
note.  Remember  that  the  Root  of  the  chord  of  the  di- 
minished seventh  is  the  same  as  the  Root  of  the  Dominant 
harmony  from  which  it  is  derived ;  therefore,  to  find  the 
Root  of  a  chord  of  the  Diminished  seventh,  the  pupil  may 
proceed  as  in  §  159,  and,  having  the  Root,  the  chord 
may  be  developed  as  shown  in  §  212.)  Write  the  chord, 
and  indicate  the  root  by  the  proper  sign. 

(jf.)  Name  the  Root,  and  write  the  chord  which  shal! 
resolve  to  the  triad  of  D  minor;  of  Ab  major;  of  At> 
minor  ;  of  FJ;  of  G$;  of  A$;  Btf;  Bb;  Db;  Eb. 

(^.)      Repeat  (e)  and  (f )  at  the  keyboard. 


220. 


Exercises. 


e    e        ,7         e 


1 1 


i 


HARMONY  SIMPLIFIED. 


«. 


8. 


Exercises  in  Harmonizing  the  Scale. 
221.     Harmonize  the  scales,  using  chords  of  the   Di- 
minished seventh  where  possible,  together  with  the  chords 
previously  learned.     Try  this  exercise  also  at  the  key- 
board. 

Synopsis. 
Write  the  usual  synopsis  of  the  chapter. 


CHAPTER  X. 

CHORDS    OF    THE    AUGMENTED    SIXTH. 

222.  Most  decided  differences  of  opinion  still  exist  with 
regard  to  these  chords.  They  will  here  be  shown  to 
be  forms  of  Dominant  harmony,  or  derived  directly  from 
it.  This  exposition  will  be  found  by  far  the  simplest 


HARMONY  SIMPLIFIED. 


137 


and  most  practical,  giving  a  more  intelligible  derivation, 
and  a  wider  application,  than  is  possible  in  any  other 
way.* 

223.  The  chords  of  the  Augmented  Sixth  are  Chro- 
matically Altered  chords,  i.  e.,  chords  in  which    some 
note  has  been  changed  without  radically  modifying  the 
chord  or  its  progression.      (  See  §  246.) 

As  the  Chords  of  the  Dominant  Seventh,  the  Domi- 
nant 7th  and  9th,  and  the  Diminished  7th,  belong  to 
Dominant  harmony,  though  each  appears  in  a  different 
form  (  one  note  more  or  less ;  with  the  Root  or  without 
it;  etc.),  so  the  chords  of  the  Augmented  Sixth  are  no 
exception,  but  may  be  developed  from  Dominant  har- 
mony, as  will  be  shown. 

Construction  and  Resolution. 

224.  These   harmonies   appear  in  three  forms,  viz., 
Augmented  Six-Three,  Augmented  Six-Four-Three,  and 
Augmented  Six-Five-Three  chords,  e.  g., 


Fig.  69. 


To  Construct  the  Augmented  Six-Three  Chord. 

225.     Let  us  take  a  Dominant  seventh-chord,  for  ex- 
ample : 


,  place  it  in  its  2nd  inversion, 


*  Although  the  full  application  of  the  theories  here  advanced  is  original 
with  the  author,  there  is  abundant  authority  to  support  his  views.  The  investi- 
gations of  the  last  half-century  seem  to  converge,  but  the  results  of  research 
had  not  yet  been  systematized  and  the  practical  application  shown.  While  not 
claiming  the  discovery  of  new  principles,  it  is  here  attempted  to  arrange  and 
apply  the  truths  brought  out  by  Day,  Ouseley,  MacFarren,  Parry,  Piutti  and 
other  theorists. 


,-jg  HARMONY  SIMPLIFIED. 


omit  the  Root,  P/fc-s» ,  and  Chromatically  lower  the 

~ • 


5th  from  the  original  Root,  giving  the  chord  :  f(o) 

^ 


This  is  called  the  Chord  of  the  Augmented  Six-Three. 

The  Root  being  G,  and  the  original  chord  an  ordi- 
nary Dominant  7th,  the  natural  resolution  is  to  the  triad 

on  C  :  REre—  g^ga~  just  as  it  'would  be  if  the  note  D 

' 


were  not  altered. 

Notice  that  the  Leading-note  progresses  upward,  the 
Minor  7th  downward  (  as  in  the  ordinary  progression  of 
a  Dominant  7th  chord) ,  and  that  the  interval  of  an  Aug- 
mented 4th  is  resolved  naturally  by  further  expansion,  as  in 
chords  of  the  Dominant  7th,  Diminished  7th,  and  Minor 
pth ;  while  the  5th  lowered  by  an  accidental  follows  the 
natural  tendency  downward.  The  characteristic  interval 
of  the  Augmented  6th,  Db-B,  from  which  the  chord  is 
named,  resolves  by  further  expansion. 

Exercises. 

Taking  in  turn  the  chord  of  the  Dominant  7th  in 
every  key,  place  it  in  its  second  inversion,  omit  the  Root, 
lower  the  5th  (from  the  Root)  by  an  accidental,  thus  form- 
ing a  chord  of  the  Augmented  Six-Three,  and  resolve  it  as 
shown  above. 

To  Construct  the  Augmented  Six-Four-Three 
Chord. 

226.  If  the  same  Dominant  seventh-chord  is  taken  in 
its  second  inversion  as  before,  but  this  time  without  omit- 
ting the  Root,  and  the  5th  lowered  as  above,  we  shall 
have  the  same  Augmented  Sixth-chord  as  before,  with 

I    Q 
the  addition  of  the  Root,  G  :  EScizfc:.     This   is  called 


HARMONY  SIMPLIFIED. 


the  Chord  of  the  Augmented  Six-Four-Three.  For  pre- 
cisely the  same  reasons  as  the  Augmented  Six-Three 
chord,  the  natural  resolution  is  to  the  triad  on  C : 


Exercises. 

(a.)  Taking  in  turn  the  chord  of  the  Dominant  yth 
in  every  key,  place  it  in  its  second  inversion,  not  omitting 
the  Root,  lower  the  5th  (from  the  Root),  thus  forming 
a  chord  of  the  Augmented  Six-Four-Three,  and  resolve 
it  as  shown  above. 

(3.)     Repeat  the  above  at  the  keyboard. 

To  Construct  the  Augmented  6-5-3  Chord. 

227.     If  we  take  the  same  Dominant  harmony  as  be- 
fore, this  time  with  \heMtnor  qth  from  the  Root  added^ 

?- 

? — ,   place   it  in  its  second   inversion,   omit  the 

Root,  and  lower  the  5th  (  from  the  Root )  by  an  acci- 

r-Q- 

dental,  we  shall  have  the  chord  :  F?q\-bgg~T    called    the 


Augmented  Six-Five,  which  has  the  characteristic  of  sound- 
ing like  a  Dominant  seventh-chord.  This  chord,  being 
derived  from  the  same  harmony  as  before,  though  in  a 
fuller  form,  has  the  same  natural  resolution  to  the  triad 


But  here  are  consecutive  5ths,  which  may  be  avoided 
in  various  ways.  Among  them  may  be  mentioned  :  (  a  ) 
Resolving  first  to  an  Augmented  |  or  i,  which,  being  pre- 
cisely the  same  harmony,  does  not  affect  the  character  of 
the  final  resolution:  or  (3)  delaying  the  resolution  of 


I40  HARMONY  SIMPLIFIED. 

some  of  the  parts,  thus  forming  a  chord  of  the  f  on  trfe 
Subdominant  before  the  common  chord  enters.  Both 
ways  are  exemplified  in  Fig.  70. 

i       ^i  i_     ;  .*-•  i  ___r.^ • r%-fii*'^ —  /  w  \  ^  '    •  — l~ 


I  V  IV     I 

Exercises. 

(a. )  Taking  in  turn  the  chord  of  the  Dominant  yth 
in  every  key,  add  the  Minor  9th,  place  it  in  its  second  in- 
version, omit  the  Root,  lower  the  5th  (from  the  Root)  by 
an  accidental,  thus  forming  a  chord  of  the  Augmented 
Six-Five-Three,  and  resolve  it  as  above. 

(6.)     Repeat  the  above  at  the  keyboard. 

228.  The  chord  of  the  Augmented  Six-Three  is 
called  the  Italian  Sixth ;  the  chord  of  the  Augmented 
Six-Four-Three  is  called  the  French  Sixth ;  and  the  chord 
of  the  Augmented  Six-Five-Three  is  called  the  German 
Sixth. 

In  the  Italian  Sixth,  there  being  but  three  notes,  it 
is  necessary  to  double  one  of  them.  The  best  one  to 
double  is  the  7th  from  the  true  Root.  (  N.  B.  It  is  quite 
proper  in  this  case  to  double  the  yth,  since  by  the  omis- 
sion of  the  Root  the  downward  tendency  of  the  7th  is  less 
marked  than  if  it  were  present.) 

Another  reason  is,  that  the  lowering  of  another  note  by 
an  accidental  disturbs  the  feeling  of  Tonality,  so  that  the 
7th  does  not  seem  to  have  the  full  tendency  downward. 
(See  "How  to  Modulate,"  §§  44  and  45.)  The  ten- 
dencies thus  having  been  removed  or  modified,  can  hardly 
be  said  to  have  been  violated. 

N.  B.     The  pupil  should  now  review  chapters  V  to 


HARMONY  SIMPLIFIED. 


141 


X,  especially  comparing  §§  157,  173,  177,  179,  180,  205, 
211,  and  224-228.  He  must  not  fail  to  understand 
practically  that,  as  asserted,  the  Chords  of  the  Dominant  yth, 
Diminished  yth,  Major  and  Minor  gth,  and  the  three  forms  of  the 
Chord  of  the  Augmented  6th,  are  nothing  more  than  different  forms 
of  the  same  Fundamental  harmony,  derived  from  the  same  Root, 
having  the  same  dissonant  intervals,  and  the  same  resolution. 

NOTE.     All  chords  of  the  Augmented  sixth  are  properly  classed 
among  the  Altered  chords.    ( See  Chapter  XI.) 

Chord  of  the  Augmented  Sixth  derived  from  the 
Supertonic. 

229.  There  is  another  chord  of  the  Augmented  Sixth, 
which,  although  it  is  not  strictly  in  the  key,  is  in  such 
common  use  that  it  will  be  mentioned  here. 

The  chord  in  question  is  the  one  which  resolves  to 
the  Chord  on  the  Dominant.  Therefore,  its  Root  should 
be  found  a  4th  lower  than  the  Dominant,  i.  e.,  on  the 
Supertonic.  In  order  to  have  exactly  the  form  of  a  Dom- 
inant seventh  and  ninth-chord  (  which  must  be  exact  in 
all  its  intervals  if  it  is  to  serve  as  the  basis  of  an  Aug- 
mented Sixth-Chord),  the  3rd  from  the  Root  must  be 
Major.  Therefore,  in  Fig.  71*  F  must  be  made  sharp, 
though  the  signature  does  not  require  it.  The  Minor  9th 
from  D,  which  is  necessary  for  the  Six-Five  form,  is  El?, 
which  also  is  not  indicated  by  the  signature.  Thus  this 


chord  LjsL—<g —  is  not  so  strictly  in  the  key  as  are  the 

above  examples. 

Taking  this  chord  as  the  basis,  by  placing  it  in  its 
second  inversion  and  lowering  the  5th  from  the  original 
Root,  which  Root  is  to  be  omitted  (  remember  that  the 
Root  is  D),  we  shall  have  a  Chord  of  the  Augmented 
Sixth,  which  resolves  to  the  Dominant. 


142 


HARMONY  SIMPLIFIED. 


Fig.  7 1 , 

L.^_ 

r 

a  o 

II  II  II  II 

In  Fig.  71  are  shown  the  various  forms  of  |'  f',  and  f, 
at  (a),  (6)  and  (c).  The  consecutive  5ths  at  (c)  may 
be  avoided  as  shown  in  ( d  ),  and  as  mentioned  in  §  227. 

230.  This  chord  was  discovered  and  used  before  the 
one  derived  from  the  Dominant  (Fig.  69  ),  and  was  long 
considered  the  only  one  in  the  key.       But,  as  just  seen,  it 
is  not  so  strictly  in  the  key  as  the  one  derived  from  the 
Dominant,  as  there  are  no  less  than  three  altered  notes 
in  the  Six-Five  form,  and  two  altered  notes  in  the  other 
forms.      (  For  further  explanation  of  Augmented  Sixth- 
Chords  see  "  How  to  Modulate,  "  Chapter  V.) 

Exercises. 

231.  (a)     Form  chords  of  the  Augmented  Sixth  (in 
three  forms)  upon  the  Supertonic  of  all  keys,  and  resolve 
them  to  their  Dominant  triads  as  shown  in  Fig.  71- 

The  pupil  must  not  fail  to  follow  the  process  given 
in  §  229,  of  starting  from  a  given  Root,  building  the 
chord  of  the  7th  (or  7th  and  9th,  as  may  be  required), 
not  forgetting  that  the  3rd  from  the  root  is  to  be  raised 
by  an  accidental,  placing  it  in  its  second  inversion,  omit- 
ting the  root  or  not  as  required,  and  lowering  the  5th 
from  original  root. 

(3.)     Repeat  the  above  at  the  keyboard. 


232. 

1.      R.  s^j,   I      „    e 

Exercises. 

-                         7 
8   0     f      9       6,     7       t 

i  t 

-*-)Tjtj  

* 

^ 

\— 

^         \    f?       ,-D 

^^ 

—  _,    ^2 

v-^  v  — 

\ 

^—&— 

1             1 

~^—&- 

~\  & 

- 

\~\  —  ' 

HARMONY  SIMPLIFIED. 


2. 


LI  li  f  * 


N.  B. 


3. 


a   7 


5      2 


6  7 


N.  B. 


4.  -  3  3 


5.      J.    5 


8  7 
f   - 


6.      J-    -£- 


6047  6        ^7  ^, 


ftff 


O0      $ 


1 


n 


7.      J'       8 

i 

t: 


607.  7 


r-;§ p' — r~      Tel 

g^^^ 


e      7b        8  sb    7  es 


I 


144 


HARMONY  SIMPLIFIED. 


233.  Sometimes   the  Augmented  Sixth-Chord  upon 
the  Supertonic,  instead  of  resolving  directly  to  the  Dom- 
inant, progresses  to  the  Tonic  Six-Four  Chord,  which 
is  thus  interposed  between  the  Augmented  Sixth  and  its 
natural  resolution,  the  Dominant.     This  is  the   case  at 
the  points  marked  N.  B.  in  the  second  and  third  exer- 
cises in  §  232. 

Exercises  in  Harmonizing  the  Scale. 

(a.)  Harmonize  the  scales,  using  chords  of  the 
Augmented  6th  where  possible,  together  with  all  the 
chords  previously  learned. 

(<5.)     Try  these  exercises  also  at  the  keyboard. 

Exercises. 

234.  Compare  the  formation  of  the  different  chords 
with  each  other  as  shown  in  §  228,  and,  taking  any  note 
for  a  Root,  try  to  develop  the  different  chords  from  that 
Root.     Repeat  this  exercise  at  the  keyboard. 

Synopsis. 

Write  the  usual  synopsis  of  the  chapter. 

Recapitulation. 

235.  It  cannot   be  too  strongly  impressed,  that  the 
whole  harmonic  system  is  a  process  of  building  from  a 
Fundamental,  or  Root.     From  the  Prime  tone  is  devel- 
oped the  triad,  by  adding  a  3rd  and  5th.     The  Chord  of 
the  Seventh  is  formed  by  the  addition  of  another  note ; 
and  the  Chord  of  the  Ninth  by  still  another.     The  chord  of 
the  Diminished  Seventh  is  formed  from  the  Chord  of  the 
Minor  Ninth  by  the  omission  of  the  Root.     The  Chord  of 
the  Augmented  Sixth  is  formed  by  inverting  the  Chord  of 
the  Minor  Ninth  and  Chromatically  Altering  the  5th  from 
the  Root.      The  triad  is  the  foundation  of  all  chords. 


HARMONY  SIMPLIFIED. 


1*5 


The  following  Synopsis  of  Chords  shows  this  in 
detail. 


'  Minor 

uiminisnea  ytn. 

6 
'Aug., 

9th. 

o 

FUNDA-    r 

MENTAL, 

The 

Domi- 
nant 7th.  ' 

Aug- 
mented ' 
6th. 

6 

Aug.4 

3 

PRIME 

>  Triad.  ^ 

TONE, 

^  Major  9th.            *>Aug.6 

or 

5 

ROOT. 

(               ( 

Secondary  7ths.                                 3 

236.  It  will  be  further  observed  that 

(a.)  The  natural  resolution  of  all  Dependent  chords  is  gov- 
erned by  the  same  Tendencies  and  Influences. 

(  b.)  The  same  laws  of  Part-leading  control  the  connection 
of  all  chords,  Independent  or  Dependent. 

(c.)  Dependent  chords  may  sometimes  progress  without  ca- 
dencing  resolution,  in  which  case  they  are  governed,  not  by  the 
laws  of  natural  resolution,  but  by  the  laws  of  part-leading  in 
chord-connections  as  in  Independent  chords. 

237.  From  a   consideration  of  the  above  it  will  be 
seen,  that  the  different  chords  are  but  different  forms  or 
manifestations  of  the  same   Primary  chord.     It  is,  there- 
fore, but  logical  that,    as  above   shown,   the  same   laws 
should  govern  all  the  forms.     The  Harmonic  System  is 
wonderfully  simple,  yet  complete. 


HARMONY  SIMPLIFIED. 


CHAPTER  XL 

ALTERED  CHORDS  :  FUNDAMENTAL  CHORDS. 

How  to  Distinguish  them;  Their  Roots  and  Keys. 
238.     Any   note   of   a  chord    may   be    Chromatically 
raised   or   lowered;    e.    g., 


When  this  occurs,  certain  changes  take  place  which 
render  it  necessary  to  consider  the  chord  from  a  new 
point  of  view.  To  enable  the  pupil  to  understand  the 
changes  which  take  place,  it  is  necessary  to  study  the 
following. 

Preliminary  Premises. 

239-  (  *•)  Fundamental  chords  (i.e.,  chords  like 
Dominant  chords,  also  like  Nature's  chord),  can  be 
built  upon  any  and  every  note.  (See  §91.)  Funda- 
mental chords  may  appear  as  triads,  Chords  of  the  7th,  of 
the  Diminished  7th,  of  the  Major  9th,  or  the  Minor  9th. 
They  must  have,  counting  from  the  Root,  a  Major  3rd, 
a  Perfect  5th,  a  Minor  7th  (  if  a  chord  of  the  7th  ),  and 
a  Major  or  a  Minor  9th  (  if  a  chord  of  the  9th) .  Or,  for 
convenience  in  comparing,  the  chord  may  be  described 
by  describing  the  successive  3rds  when  the  chord  is  in  its 
Direct  form,  as  follows : — 

From  i  to  3  is  a  Major  3rd,  from  3  to  5  is  a  Minor 
3rd,  from  5  to  7  is  a  Minor  3rd,  and  from  7  to  9  is  either 
a  Major  or  a  Minor  3rd  according  to  the  key.  Placed 


HARMONY  SIMPLIFIED.  147 

one  above  the  other  as  in  the  chord,  it  may  be  expressed 
as  follows  : — * 

9-. 

>  Major  or  Minor. 

7 

y  Minor. 

5 


[•  Minor. 

3) 

>  Major. 

i  ' 


This  might  be  called  the  Formula  for  constructing 
Fundamental  chords,  since  they  must  correspond  exactly 
with  it  in  order  to  be  Fundamental. 

Exercises. 

240.  Form  Fundamental  chords  in  the  four  forms  mentioned,  up- 
on all  notes  of  the  Chromatic  scale,  and  compare  them  with  the 
formula. 

241.  (2.)     Fundamental  Dependent  chords,  like  Dom- 
inant chords,  whether  appearing  as  Chords  of  the  yth, 
Diminished  7th,  or  of  the  pth,  resolve  naturally  to  the  triad 
a  4th  higher.      (  See  foot-note,  §  158.) 

242.  (3.)     All  Fundamental  chords  are  considered 
as  built,  each  upon  a    particular  Root.      The  chord  of 
resolution  is  a  4th  highei  than  this  Root,  in  every  case. 

243.  (4-)     Change  of  Root.     This  can  best  be  ex- 
plained by  illustration.     By  reference  to  §  241,  it  becomes 
apparent    that   the  natural  resolution  of   any  dependent 
chord  is  to  the  triad  a  4th  higher. 

Reference  to  Fig.  68  and  the  accompanying  text 
shows  that  the  same  notes  (  on  the  keyboard  )  may  be 


*  If  the  Root  is  omitted,  as  in  the  chord  of  the  Diminished  seventh,  the 
Major  jrd  from  i  to  3  will  not  be  present  in  the  formula. 


148  ffARMONY  SIMPLIFIED. 

derived  from  different  Root-notes,  the  only  difference  be- 
ing in  the  manner  of  writing  the  chords,  i.  e.,  the  nota- 
tion. 

It  may  be  said,  conversely,  that  the  different  nota- 
tion shows  that  the  chords  spring  from  different 
Roots.  To  illustrate,  (  a  )  and  (  b  )  of  Fig.  72  are 
alike  in  sound.  But,  if  a  chord  of  the  Diminished  yth 


is  built  upon  the  Root  G,  it  will  be  like  (  a  ),  while  a 
similar  chord  erected  upon  the  Root  Aj  will  be  like  (  b  ) 
when  inverted.  The  two  chords,  which  sound  alike, 
have  different  notation  because  they  are  erected  upon 
different  Roots.  Reference  to  §  211  will  show  that 
their  resolutions  differ  radically.  This  is  on  account  of 
the  law  of  Tendencies  shown  in  §  152,  viz.,  the  Leading- 
note  tends  toward  the  Tonic,  the  fourth  degree  of  the 
scale  tends  downward,  and  the  chief  dissonance,  the  Di- 
minished yth  between  the  Leading-note  and  the  9th  from 
the  original  Root,  tends  to  contract.  Therefore  we  may 
say  that,  by  the  change  of  notation,  the  Root  is  changed, 
and,  consequently,  the  resolution  is  also  changed. 

Therefore,  if  we  would  have  a  proper  resolution, 
the  chord  must  be  so  written  as  to  show  which  note  is 
the  Leading-note,  which  the  gth  from  the  original 
Root,  etc.,  in  order  to  know  how  to  apply  the  law  of 
Tendencies. 

244.  In  §  243  is  shown  how  a  change  of  notation, 
or  Enharmonic  change,  as  it  is  called,  implies  a  change 
of  Root,  even  where  the  notes  on  the  keyboard  remain 
the  same.  In  cases  where  one  or  more  notes  are  really 


HARMONY  SIMPLIFIED.  ^ 

altered  by  accidentals,  the  change  of  Root  is  even  more 
clearly  apparent.     For  example,  ~fa~%^n.  is  the  chord 


of  the  Dominant  yth  on  the  Root  G,  resolving  to  the  triad 
of  C.      If    the    note     G   in    this    chord  is  chromatically 


raised,  thus  :    ifeiggzn,  the  chord  is  like  the  chord  of  the 

Diminished  7th  built  upon  the  Root  E  (which  is  of  course 
omitted  ),  resolving  to  the  triad  on  A.  Therefore,  the 
Root  of  the  chord,  as  well  as  the  resolution,  may  be  said 
to  have  been  changed  by  the  alteration  of  the  single  note. 
Consequently : 

245.  (  5.)     By  a  change  of  Root  a  change  in  the  res- 
olution is  necessarily  caused. 

Now   we   will   proceed   to    consider    the    Altered 
chords. 

246.  By  reference  to  the  foot-note,  §  158,  it  becomes 
clear  that  the  natural  resolution  of  any  dependent  chord 
is  to  the  triad  a  4th  higher  than  the  Root  of  that  Depen- 
dent chord ;  and  we  have  just  seen  that  when  through  a 
change  of  notation,  or  other  causes,  the  Root  is  changed, 
the  natural  resolution  of  the  chord  is  completely  changed 
in  consequence.      This  fact  is  illustrated  in  Fig.  68  and 
the  accompanying  text. 

A  change  in  a  chord,  whether  of  a  note  or  simply 
in  the  notation,  which  produces  a  change  of  Root  (  and 
therefore  of  resolution),  is  called  an  Harmonic  change. 
Where  the  change  simply  affects  one  part  transiently, 
not  producing  a  change  of  Root  and  resolution ,  the 
change  is  called  a  Afclodic  change. 

Where  a  chromatic  change  in  a  note  is  made  as  sug- 
gested in  §  238,  the  result  must  be  one  of  two  things : 


,50  HARMONY  SIMPLIFIED. 

either  the  Harmonic  change  just  mentioned,  or  the  Me- 
lodic change. 

By  an  Harmonic  change  a  completely  new  chord  is 
formed,  which  is  outside  the  key,  speaking  strictly,  since 
it  contains  a  note  foreign  to  the  scale  of  the  key.  Such 
changes  will  be  considered  under  the  head  of  Foreign 
Chords,  Chapter  XII. 

By  a  Melodic  change  the  alteration  has  more  to  do 
with  a  single  part,  rather  than  effecting  any  change  in 
the  character  of  the  chord.  Such  changes  produce  Al- 
tered chords,  if  they  have  sufficient  duration  to  be  consid- 
ered as  chords  ;  or  Passing-notes,  if  of  insufficient  duration. 
Such  alterations  may  occur  in  Chords  of  the  7th  as  well 
as  in  triads. 

But  the  pupil  will  desire  to  distinguish  between  Al- 
tered chords  and  Foreign  chords,  and  to  discover  the 
Roots  and  resolutions  of  the  Foreign  chords.  The  fol- 
lowing is  the  method  : — 

To  Distinguish  between  Altered  Chords  and 
Foreign  Fundamental  Chords. 

247.  (  I.)  For  convenient  survey,  place  all  the  notes 
within  the  compass  of  one  octave,  striking  out  all  dupli- 
cates. 

(  2.)  Place  the  chord  in  3rds.  (  See§  172.) 
(  3.)  Construct  a  descriptive  formula  of  the  3rds  as 
shown  in  §  239,  and  compare  it  with  the  formula  of  a 
Fundamental  chord  there  shown.  If  they  correspond, 
the  chord  in  question  is  a  Fundamental  chord.  If  not,  it 
is  clear  that  either  it  was  not  originally  a  fundamental 
chord,  or  that  some  interval  has  been  altered.  (  If  the 
Root  of  such  a  chord  is  unknown  to  the  pupil,  he  must 
discover  the  altered  note  or  notes  by  comparison  with  the 
formula  before  proceeding  to  find  the  root  by  the  method 


HARMONY  SIMPLIFIED. 


outlined  in  the  following  paragraph.)     But,  before  pro- 
ceeding, let  us  illustrate  the  above. 


248.     For  example,  to  find  whether 


is  a  Fundamental*  or  an  Altered  chord :  — 

Placing  all  the  notes  within  the  compass  of  one  octave, 


gives  :    j-g^- — ^ — .       Inverting,   to    obtain  the  required 
figuring,  we  have  successively : 


the  last  being  the  required  form. 

Describing  the  yds  as  required  in  §  239,  we  have 
the  formula    7 

5 


V  minor. 


>•  minor. 

H 

>  minor, 
i  ' 


*  It  should  be  noticed  that  the  Dominant  Is  the  only  Fundamental  chord 
of  the  Seventh  which  is  to  be  found  in  any  key.  The  Secondary  Sevenths  do 
not  correspond  perfectly  in  their  intervals  with  the  intervals  of  the  Fundamental. 
(  This  accounts,  in  part,  for  the  prominence  given  to  the  various  forms  of  Dom- 
inant harmony.) 

Chords  which  are  not  Fundamental  chords  may  be  Secondary  chords. 
Therefore,  if  the  formula  does  not  correspond  with  the  formula  for  a  Funda- 
mental chord,  we  should  compare  it  with  the  Secondary  chord  having  the  same 
Root  (provided  that  the  given  Root  represents  a  Secondary  chord)  before 
deciding  that  it  is  an  Altered  chord. 


I  HARMONY  SIMPLIFIED. 

Comparing  with  the  standard  formula : — 
Standard  Formula  of  the 

Formula :  Given  Chord : 

9)  * 

>  major  or  minor minor 

}mi, 


minor •  minor 

5  V 

|-  minor minor 

3  I       • 
>•  major 

i  ' 

we  find  it  agrees  with  it  in  every  particular,  as  far  as  it 
goes.  It  is  therefore  a  Fundamental  chord  without  its 
root,  i.  e.,  a  chord  of  the  diminished  yth. 

Again,  to  learn  whether  the  chord  E^ztggz:^    is    a 


Fundamental  chord  or  not : —  Proceeding  as  before  gives 
the  formula :        >•  major. 
(•  minor. 

3  I 

>•  major. 

i  ' 

Comparing  this  with  the  standard  formula,  we  find 
that  the  intervals  of  the  given  chord  cannot  be  made  to 
correspond  with  three  successive  intervals  in  the  standard 
formula.  Thus 

Standard  Formula  of 

Formula :  Given  Chord : 

9)  (7 

>•  major  or  minor     .     .     .     major  -j        :  corresponds. 

7  5 

J-  minor minor  -j        :  corresponds. 

5'  i 
)  (  ** 

>•  minor major  •<        :  does  not  cor- 

3  \  '-i          respond. 


HARMONY  SIMPLIFIED. 


'53 


Therefore,  even  if  the  Root  of  the  given  chord  were 
found,  whatever  note  it  might  be,  it  could  never  form  a 
Fundamental  chord  in  connection  with  the  notes  as 
given.  Comparison  with  the  chords  of  the  yth  upon  the 
various  degrees  of  the  scale,  by  comparing  the  formulae, 
shows  that  this  chord  might  be  the  Chord  of  the  7th 
upon  the  ist  degree  of  the  scale  of  Bi?  major,  resolving 
naturally  to  the  triad  upon  the  4th  degree ;  e.  g., 


Exercises. 

State  whether  the  following  chords  are  Altered 
chords,  or  Fundamental  chords,  or  whether  they  might 
be  secondary  chords  in  some  key  : — 


To  Discover  the  Root  of  any  Fundamental  Chord. 

249.  (  i.)  Write  all  the  notes  in  the  compass  of  one 
octave,  striking  out  duplicates.* 

(  2.)     Place  the  notes  in  3rds,  as  shown  in  §  247. 

(3.)  If  it  is  a  triad  (three  notes),  the  Root  will 
be  the  lowest  tone.  (  This  is  merely  the  result  of  the  defi- 
nition of  the  Direct  form  of  a  chord.  See  §  125.)  It 
will  now  be  apparent  whether  the  chord  is  (  I  )  an  ordi- 
nary Major  or  Minor  triad  ;  (  2  )  an  Altered  triad ;  or  (3  ) 
an  incomplete  form  of  a  Fundamental  Dependent  chord. 


*  Sometimes  a  note  is  omitted  in  a  Chord  of  the  7th,  or  7th  and  9th.  The 
pupil  should  refer  to  §  248,  and  observe  how  the  intervals  in  the  Fundamental 
chord  would  occur  if  the  Root  were  omitted;  for  without  the  Root  a  different 
order  of  intervals  would  result,  which  might  lead  the  pupil  to  think  a  chord  to 
be  an  Altered  chord  when  in  reality  it  is  an  incomplete  form  of  a  Fundamental 
chord. 


154 


HARMONY  SIMPLIFIED. 


N.  B.  Remember  that  a  Diminished  triad  may  be 
considered  as  an  incomplete  form  of  a  Chord  of  the  7th, 
and  resolve  accordingly.  (See  §  179-) 

250.  If  it  is  a  Chord  of  the  Seventh  (four  notes  ),  we 
must  first  be  sure  that  it  is  a  Fundamental  and  not  an 
Altered  chord.     How  to  accomplish  this   is  shown  in 
§  247.     If  shown  to  be  a  Fundamental  chord,  either  with 
or  without  the  Root,  we  may  proceed  as  follows  : —  Com- 
pare the  notes  as  shown  in  §  29,  to  discover  which  note 
is  relatively  the  "  sharpest"  and  which  the  "flattest." 

In  comparing  the  notes,  the  sharpest  one  will  be 
the  Leading-note.  (  The  Jlattest  note  will  be  the  9th, 
if  it  is  a  Chord  of  the  9th,  otherwise  it  will  be  the  7th.) 
The  Leading-note  being  a  Major  3rd  above  the  Root  of  a 
Fundamental  Dependent  chord,  to  find  the  Root  when  the 
Leading-note  is  known  simply  count  a  Major  3rd  down- 
ward from  that  Leading-note.  (  N.  B.  The  Root  may 
not  be  present  in  the  chord.  It  never  is  in  chords  of  the 
Diminished  7th.)  When  the  Root  is  found,  it  can  be 
proven  by  the  "  flattest"  notes,  which  should  be  the  9th 
or  the  7th  from  the  Root  as  above  shown.  (  For  further 
explanation  of  this  point,  see  "  How  to  Modulate," 
p.  18.) 

251.  Illustration  of -preceding  Section.     To  find  the 
Root  of  pijazi^:^.     Comparing  the   notes  to  find  the 


"sharpest"  note,  we  see  that  B  is  represented  by  five 
sharps ;  D  by  two  sharps ;  F  by  one  flat ;  and  Ab  by  four 
flats;  consequently  B  is  the  "sharpest"  note,  and  there- 
fore the  Leading-note.  As  the  Root  of  the  chord  should 
be  a  Major  3rd  below  the  Leading-note,  by  counting 
downward  a  Major  3rd  from  B  we  find  that  G  is  the  Root 


HARMONY  SIMPLIFIED. 


'55 


of  the  chord.  Building  u  Fundamental  chord  upon  the 
Root  G,  we  have  G-B-D-F-Afr,  which  is  a  chord  of  the 
Minor  9th,  and  corresponds  to  the  notes  of  the  given 
chord.  Therefore,  the  chord  in  question  is  a  Chord  of 
the  Diminished  yth  upon  the  Root  G,  resolving  to  the 
minor  or  major  triad  on  C.  (  See  §213.) 

Again,   to  find  the   Root  of  the    chord 


Comparing  as  before,  we  find  that  Cfr  is  represented  by 
seven  flats ;  D  by  two  sharps ;  F  by  one  flat ;  and  A]?  by 
four  flats;  consequently,  D  is  the  "sharpest"  note.  A 
Major  3rd  below  D  is  Bi?,  which  is  consequently  the 
Root  of  the  chord.  Placing  the  chord  in  3rds,  and 
writing  the  Root  in  its  place,  the  full  chord  is  seen  to  be 
a  Chord  of  the  Minor  pth  upon  the  Root  BJ?. 

252.  To  discover  in  'what  key  such  a  foreign  chord 
is  written,  simply  remember  that  the  "sharpest"  note 
is  the  Leading-note,  or  yth  degree  of  the  scale.  There- 
fore, the  chord  hffkHTgp13  may  be  said  to  be  written  in  the 


key  of  C  minor,  and  the  chord  Kiftr-bz?  -  m  the  key  of 

— 


minor.      (  See  also  "  How  to  Modulate"  §  20.) 

Exercises. 

253.     Name   the    Roots  and  Keys  of   the   following 
chords  :  — 


Ambiguous  Chords. 

254.     .Sometimes  a  chord  may  occur  which  might  be 
either   an   Altered   chord   or  a  Foreign  chord.     E.  g., 


i56 


HARMONY  SIMPLIFIED. 


F#-C-D#  might  be  either  a  chord  derived  from  the  Sec- 
ondary 7th  on  the  2nd  degree  of  C  Major  (  by  raising  F 
and  D  by  accidentals ; —  notice  that  the  chord  appears 
without  the  5th ; — write  it),  or  it  might  be  considered  as 
derived  from  a  new  Root,  B,  being  an  incomplete  form  of 
the  Chord  of  the  Diminished  7th  (  write  it). 

To  learn  which  of  two  Roots  is  intended,  examine 
the  resolution :  for  if  the  resolution  is  the  same  as  it 
would  have  been  without  the  alteration,  it  proves  that 
the  chord  is  Altered ;  whereas,  if  the  resolution  is  differ- 
ent, it  shows  that  the  chord  is  a  Foreign  chord.  .  For 
example,  in  the  above,  if  the  Altered  chord  derived 
from  the  Root  D  is  intended,  the  progression  would 
be  to  the  chord  G— C— E,  which  is  considered  as  inter- 
polated* between  the  chord  on  D  and  its  natural  reso- 
lution which  follows.  (See  a,  Fig.  73.)  If  the  Root 
B  is  intended,  the  resolution  would  be  to  the  minor  triad 
on  E  (  a  4th  higher  than  B) .  (  See  b,  Fig.  73.) 


Fig.  73.  PE5- 


Root: 


*  By  an  interpolated  chord  is  meant  a  chord  placed  between  two  chords 
which  naturally  belong  together.  For  example,  the  natural  resolution  of  the 
seventh-chord  upon  D  is  to  the  triad  on  G.  But  the  chromatic  alteration  of  the 


-  —  *&5i  —  ,  inclines  it  away  from  its  place  in  the  chord  of 


note  D,  thus : 


G,  and  would  cause  an  awkward  effect  should  it  return  after  starting  else- 
where. Consequently,  the  triad  on  C  is  interpolated  for  smoother  effect  ;  but 
the  true  resolution  is  only  delay  'ed,  for  it  enters  immediately  after.  (See 
Fig-  73,  <*.) 


HARMONY  SIMPLIFIED. 


'57 


Treatment  of  Altered  Chords. 

255.  As  mentioned,  any  note  of  a  chord  may  be  al- 
tered by  an  accidental ;  and  when  the  resulting  change 
does  not  cause  a  change  of  Root,  it  is  called  simply  an 


Altered  chord ;  e.  g.,  pEKH^zz:  is  the  common  triad  on 

C  ;  if  the  note  G  is  raised  chromatically,  thus  : 

we  say  that  the  note  G  has  been  altered  from  its  original 
condition,  and  the  whole  triad  might  be  called  an  altered 
triad.  The  triad  has  not  been  essentially  changed  (we  still 
look  upon  C  as  the  root) ,  but  the  note  G,  having  been 
raised,  is  strongly  inclined  to  progress  to  the  next  note 
above,  A.  Such  alterations  may  occur  in  seventh-chords 
as  well  as  in  triads. 

256.  The  pupil  needs  little  guidance  in  the  treatment 
of  Altered  chords,  other  than  to  remember  that  the  ten- 
dency of  a  chromatically  raised  note  is  to  ascend,  and  the 
tendency  of  a  chromatically  lowered  note  is  to  descend. 
The  general  rule  that  accidental  sharps  tend  upward,  and 
accidental  flats  downward,  is  good  to  remember,  but  it  does 
not  convey  the  whole  idea,  for  a  natural  may  have  the 
effect  of  raising  a  note  previously  flatted  by  signature  or 

accidental ;  e.  g.,  p^fr— *.      \      .    The  natural  here  raises 


the  El?  chromatically,    and  is  similar  to :  K8 

In  the  same  way,  a  natural  may  chromatically  lower  a 

note  :  e.  g.,  U/lffit"     ^      Qi*    •     Thus  it  is  clear  that  flats, 


naturals  and  sharps   are    relative   rather   than   specific 
terms. 


i58 


HARMONY  SIMPLIFIED. 


A  chromatically  altered  note,  being  a  tendency-note, 
should  not  be  doubled. 

Altered  Chords  in  General  Use. 
257.     Of  the  many  altered  chords,  those  most  in  use 
are : 

(  a.)     The  Triad  with  raised  5th  ; 

(  b.)     The  Chord  of  the  yth  with  raised  5th ; 

(  c.)     The  Chords  of  the  Augmented  6th  ; 

(  </.)    The  Neapolitan  6th.      (  See  §  259.) 

The  progression  of  these  chords  is  usually  the  same 
as  if  the  unaltered  intervals  were  present ;  while  the  pro- 
gression of  the  altered  notes  depends  upon  the  tenden- 
cy of  the  accidental  alteration.  The  changes  are  simply 
melodic  changes  of  a  single  part,  for  the  purpose  of 
variety  or  of  softening  a  harsh  effect. 

Exercises. 

(fl.)     Write  examples  of  all  the  above-mentioned 
Altered  chords  in  various  keys. 


258. 


_6_5|     5    5$    36         6 

"ZL 


F^TTh f~<5>— F— — - — F^ 

p2=fca=|=^^=y 


3.       R-    3       I   2*  6     7         g  I 


6        7        7 


HARMONY  SIMPLIFIED. 


4.  _5l_5  _    3    58    5    -  6_    3    5$     6  6  6 

^^^fS=ff^f=  -f=^=(=f= 


6 

6    * 


7  50  7 


3  502  6 


-^fr— g — flzJ — - 


1 


6.      J- 


5  507 


Jfl 

7.       J-          ^075508767505055ljf  50 


8.       J- 


0  *.  30 

=4 


Bii  E     =P^     tf.0  ~ 


=£ 


Open  Position. 

Jft    —  4    $ 

8  If  6*5022 


i6o 


HARMONY  SIMPLIFIED. 


Close  Position. 
e 

1O.     J*          8     e     t  -     t       65  7087       706    ft]      87 


PS 


Open  Position. 
11.    J. 


a       5  5(5 

~^5         P*^ 


35         5    5fl 


*=£ 


F 


&t 


—G>— 


-sr- 

Advanced  Course. 

Neapolitan  Sixth. 

259.     (  Usual  explanation.    For  author's  exposition  of  the  chord,  see 
§  261.) 

Among  the  altered  chords  is  one  in  such  common  use  as  to  receive 
a  distinctive  name.     When  the  triad  on  the  2nd  degree  of  the  Minor 

' '  """^ —      ~  ~:*u  its  Root  lowered  by  an  accidental 


is  used  in  its  first  inversion, 


a  very  soft  effect  is  pro- 


duced.    The  chord  is  considered  effective  only  in  this  inversion,  and  is 
called  the  Neapolitan  Sixth ;  e.  g., 


Fig.  74. 


=F 


f«- 


This  alteration  of  the  note  on  the  2nd  degree  is  purely  arbitrary, 
like  the  lowering  of  the  5th  in  the  Chord  of  the  Augmented  6th ;  and  it 
is  frequently  used,  probably  on  account  of  the  fact  that  the  natural  (  un- 
altered )  triad  on  the  2nd  degree  in  Minor  is  a  Diminished  triad,  and 


HARMONY  SIMPLIFIED. 


therefore  has  tendencies  of  too  pronounced  character  for  effective  use 
in  ordinary  chord-connections  (  not  resolutions  ).  It  was  found,  how- 
ever, that  by  lowering  this  note  the  apparent  tendency  was  hidden, 
making  the  chord  more  manageable. 

Keyboard  and  Written  Exercises. 

260.  Form  chords  of  the  Neapolitan  6th  from  the  triad  on  the  2nd 
degree  of  every  Minor  key,  and  resolve  them. 

Derivation  of  the  Neapolitan  Sixth-Chord. 

261.  (The  following  is  submitted  entirely  upon  the  author's  respon- 
sibility.) 

The  Neapolitan  Sixth  is  believed  to  be  a  form  of  the  Augmented 
sixth-chord,  with  sufficient  license  in  its  treatment  to  admit  of  the 
smoothest  effect  in  Minor. 

The  following  examples  will  illustrate  the  assertion  and  the  grounds 

for  the  belief. 

BANISTER. 


Fig.  75. 


EMERY. 


Fig.  76. 


-•&- 


3 


BEETHOVEN. 


Fig.  77. 


j62  HARMONY  SIMPLIFIED. 

The  license  mentioned  above  is  this  : —  That  the  notes  comprising 
the  full  chord  of  the  Augmented  6th  are  often  divided  between  two 
chords.  The  chords  marked  X  in  the  illustrations  are  the  chords  in 
question. 

If  the  chord  marked  x  in  Fig.  75  is  a  chord  of  the  Augmented  6th, 
it  is  the  5th  from  the  Root  which  is  altered  by  an  accidental.  The  al- 
tered note  being  Eb,  the  root  should  be  A.  Let  us  assume  that  the 
Root  is  A,  and  develop  the  chord  from  it.  The  chord  of  the  Minor 
9th  upon  A,  (from  which  the  Chord  of  the  Augmented  6th  is  devel- 


oped,) is      (ct) — ^>~~~~^-     Omitting  the  Root  and  lowering  the  5th, 


we  have 


Now,  this  chord  is  the  same  as  the  chord  marked  x  in  Fig.  75,  ex- 
cepting that  the  Leading-note,  Cf,  which  appears  in  the  next  chord,  is 
absent,  leading  us  to  think  that  the  notes  have  been  divided  between 
the  two  chords. 

262.  Again,  in  §  224,  the  chord  of  the  Augmented  6th  is  shown  in 
Major,  with  the  dominant  of  the  key  as  the  Root.  Notice  that,  when 
the  Dominant  is  the  Root,  it  is  the  2nd  degree  of  the  scale  which  is  the 
chromatically  altered  note.  If  the  above  assertion  is  wrong,  is  it  not 
rather  strange  that  the  note  which  is  altered  by  an  accidental  to  pro- 
duce the  chord  of  the  Augmented  6th  in  Major  should  happen  to  be 
the  same  note  that  is  so  altered  in  the  Minor  key  ?  And  is  it  not  still 
more  strange  that  the  resolution  of  the  two  chords  should  be  the 
same  ?  And  is  it  not  strange  that  the  process  of  building  a  Funda- 
mental chord  upon  the  chosen  Root  should  result  in  the  desired 
Chord  of  the  Neapolitan  Sixth  ? 

In  further  proof,  the  example  in  Fig.  76  is  offered.  Here  the  Nea- 
politan 6th,  marked  x,  which  is  built  upon  the  Root  E  (since  the  chro- 
matically altered  5th  above  the  root  is  &),  resolves  directly  to  the  triad 
'on  A  (  a  4th  higher  than  E  )  without  the  help  of  any  other  chord.  No- 
tice, however,  that  the  next  chord  comes  in  to  supply  the  Leading- 
note,  for  the  cadence  has  not  been  quite  strong  enough  without  it. 

The  next  example,  Fig.  77,  from  Beethoven,  refutes  the  idea  that 
the  chord  is  good  in  only  one  inversion.  Here  the  chords  marked  X 
have  the  chord  of  the  Augmented  6th  divided  between  them,  and  the 
notes,  though  identical  with  those  of  the  other  examples,  are  in  a 
different  inversion,  giving  an  excellent  effect. 


hstRMONY  SIMPLIFIED.  163 

It  is  submitted  that  the  example  from  Beethoven  is  as  effective 
as  the  examples  in  Fig.  75  and  76. 

The  pupil  is  recommended  to  read  §§  42—50  in  "  How  to  Modu- 
late." 

Exercises. 

263.  Form  chords  of  the  Neapolitan  6th,  from  the  Dominant  as  a 
Root,  in  ever}'  Minor  key,  and  resolve  them. 

264.  Attention  is  again  called  to  the  wonderful  simplicity  of  the 
system  of  developing  the  chords  shown  in  this  volume.     By  bringing 
the  chords  of  the  Dominant  7th,  Minor  and  Major  gth,  Diminished 
7th,  Augmented  j|,  Augmented  J.  and  Augmented  §,'  and  the  Neapol- 
itan 6th  all  urjder  one  head,  derived  from  the  same  Root,  having  the 
same  dissonant  intervals,  and  the  same  natural  resolution,  one  is  inclined 
to  accept  the  statement  that  "  There  is  but  one  chord  in  the  Universe, 
the  Common  Chord.     All  others  are  merely  additions  to  this  chord." 

Synopsis. 
Write  the  usual  synopsis  of  the  chapter. 


CHAPTER  XII. 

ATTENDANT   CHORDS. 

265.  The  object  of  this  chapter  is  to  enable  the  stu- 
dent to  recognize  some  of  those  chords  which,  though 
technically  foreign  to  the  key,  so  constantly  intermingle 
with  chords  which  belong  wholly  to  the  key.  These 
foreign  chords  have  such  a  peculiarly  close  relationship 
to  the  chords  of  the  key,  that  we  cannot  well  say  that  we 
are  in  a  foreign  key  when  they  occur,  but  that  a  foreign 
key  is  suggested  or  touched.  ( Se.e  Grove's  Dictionary  of 
Music,  Vol.  II,  p.  351.) 


164  HARMONY  SIMPLIFIED. 

The  following  chapter  will  be  developed  from  a  prin- 
ciple which  is  already  familiar  to  the  pupil,  viz., 

The  Natural  Resolution  of  Dominant  Harmony  to 
the  Tonic. 

266.  By  Dominant  harmony  is  not  meant  the  chord 
of  the  Dominant  yth  alone,  but  also  the  chord  of  the  Dom- 
inant pth  (both  Major  and  Minor),  the  Chord  of  the 
Diminished  7th.  and  the  various  forms  of  the  Augmented 
Sixth-chord,  which  are  all  forms  of  Dominant  harmony, 
and  resolve  to  the  Tonic. 

Keyboard  and  Written  Exercises. 

Preliminary  to  the  following,  and  to  enable  the 
pupil  easily  to  grasp  the  subject,  he  should  form  chords 
like  the  Dominant  Jtk,  upon  every  (  chromatic  )  degree 
of  the  scale,  and  resolve  them,  like  the  Dominant  Jth, 
to  the  triad  a  4th  higher.  Do  not  write  any  signatures, 
and  do  not  call  them  Dominant  and  Tonic  chords.  Sim- 
ply notice  that  the  Chord  of  the  yth  upon  any  note  re- 
solves to  the  triad  a  4th  higher,  and  observe  that  the  ten- 
dency of  the  seventh-chord  toward  the  triad  a  4th  higher 
is  so  strong  that  there  is  clearly  a  close  relationship  be- 
tween the  two  chords.  This  relationship  is  the  same  as 
the  relationship  of  Dominant  to  Tonic,  but  they  should 
not  be  called  Dominant  and  Tonic  unless  they  are  con- 
sidered as  belonging  to  some  key,  and  that  is  not  now 
desired.  The  object  here  is  to  shoiv  the  relationship  of 
the  two  chords,  whether  they  are  in  a  key  or  are  consid- 
ered by  themselves. 

The  intervals  of  a  chord  of  the  Dominant  7th  are  a 
Major  3rd,  a  Perfect  5th,  and  a  Minor  7th.  Therefore, 
in  forming  these  chords,  the  pupil  will  see  that  these 
intervals  are  present,  and  will  use  accidental  sharps  and 


HARMONY  SIMPLIFIED.  165 

flats  to  secure  them.      (  These  chords  are  the  same  as 
the  Fundamental  chords  described  in  the  last  chapter.) 

267.  The  next  step  is  to  learn  the  reverse  of  the  above, 
viz., —  To  find  that  chord  of  the  7th  which  shall  resolve 
to  any  given  triad,  Major  or  Minor. 

Process. 

As  a  chord  of  the  7th  resolves  naturally  to  the  triad 
a  4th  higher,  to  find  the  triad  which  shall  resolve  to  a  given 
triad,  we  simply  need  to  look  a  4th  lower  than  the  Root 
of  the  triad. 

Illustration.  To  find  the  chord  of  the  7th  which 
shall  resolve  to  the  triad  (  Major  or  Minor  )  upon  A : — 
Looking  a  Perfect  4th  below  A,  we  find  E  to  be  the  Root 
of  the  desired  chord  of  the  7th.  Completing  the  chord 
of  the  7th  upon  E,  by  the  addition  of  a  Major  3rd,  Per- 
fect 5th  and  Minor  7th,  we  find  the  full  chord  to  be : 

~,  resolving  to : 


N.  B.  Remember  that  the  chord  of  the  7th  resolves 
to  either  Major  or  Minor,  since  the  chord  of  the  Domi- 
nant 7th  of  A  Major  is  the  same  as  in  A  Minor. 

Keyboard  and  Written  Exercises. 

268.  Taking  each  (  chromatic  )  degree  of  the  scale, 
in  turn,  find  the  Chord  of  the  7th  which  will  resolve  to 
the  triad  upon  that  degree.     Complete  the  chord  of  the 
7th,  and  resolve  it  to  the  proper  triad,  as  above  shown. 

269.  The  pupil  has  now  learned,  that  there  is  a  Chord 
of  the  7th  closely  related  to  every  Major  and  Minor  triad. 
Therefore  it  would  not  be  strange  to  find,  that  these  re- 
lated chords  are  sometimes  used,  although  they  are  not, 
strictly  speaking,  in  the  key. 


1 66 


HARMONY  SIMPLIFIED. 


-tf^H^ — ' — & ™ LrSi «_J — ^» IJ 

LN^^'  £•    -^ ^-_^d_  _^D_  -X^-  -  —U  -*Q- 


Fig.  78. 


I  VI         IV 

Notice  that  the  chord  marked  x  is  not  strictly  in  the 
key  of  C,  but  is  apparently  like  the  Dominant  yth  in  the 
key  of  A.  It  does  lead  to  the  chord  of  A,  and  is  in 
so  far  like  the  chord  of  the  Dominant  yth  in  the  key  of  A. 
But  the  chord  on  A  is  in  the  key  of  C  (on  the  6th  degree) . 
Now  let  it  be  noticed  that  the  chord  marked  x  is  like  the 
chord  of  the  Dominant  yth :  but  as  there  can  be  but  one 
chord  of  the  Dominant  ^th  in  a  key,  we  must  adopt  some 
other  way  of  describing  the  relation  of  this  chord  to  the  triad 
on  A,  and  will  call  it  the  "Attendant "  chord  of  A.  (  The 
reason  for  thus  naming  such  chords  is  more  clearly  de- 
scribed in  the  author's  "  How  to  Modulate.") 

270.  From  a  consideration  of  the  above,  §§  265  to 
269,  it  is  clear  that  each  major  and  minor  triad  in  any  key  has 
its  attendant  chord.*  As  shown  in  the  following  example, 
these  attendant  chords  can  be  used  with  good  effect. 
They  are  indicated  by  [A]. 


Fig.  79, 


[A] 


*  The  triads  upon  the  7th  degree  in  Major,  and  the  2nd  and  7th  in  Minor, 
are  prohibited  from  having  [  A  ]  chords.  The  reason  for  this  prohibition  is, 
that  being  Diminished  triads,  and  therefore  not  consonant,  they  could  not  be  the 
resolution  of .  a  dissonance  (  see  §  151),  and  therefore  could  not  stand  in  the 
relation  of  Tonic,  which  would  be  required  if  they  were  to  have  [  A  ]  chords. 
(It  has  been  shown  that  although  not  Tonic  and  Dominant,  a  triad  and  its  [  A  ] 
chord  stand  in  the  relationship  of  Tonic  and  Dominant.)  For  the  same  reason, 
the  Augmented  triads  in  Minor  are  prohibited  from  having  [A]  chords. 


HARMONY  SIMPLIFIED. 


167 


vi        [A]          in      [A]        IV      [A]       V 

N.  B.  In  practical  composition,  [A]  chords  would 
not  be  so  frequently  used  as  in  the  above  example,  which 
is  given  to  show  how  the  [  A  ]  chord  of  every  Major  and 
Minor  triad  in  the  key  can  be  used. 

Keyboard  and  Written  Exercises. 

271.  (a.)     Taking  the  key  of  G,  find  in  succession 
the  [  A  ]  chords  which  shall  resolve  to  the  triads  on  n, 
in,  IV,  V,  and  vi,  proceeding  as  in  §  267. 

(  £.)  In  a  similar  way,  take  all  the  Major  and  Minor 
keys  in  turn. 

Much  repetition  and  persevering  practice  are  neces- 
sary to  give  the  required  proficiency.  Before  proceeding, 
the  pupil  must  be  able  to  give  instantly  the  [  A  ]  chord 
of  any  Major  or  Minor  triad. 

272.  It  is  remarkable  what  frequent  use  of  the  [A] 
chords   has   been   made   by  composers,  beginning  with 
Beethoven.      In  the  following  example,  from  Mendels- 
sohn's Spring  Song,  are  five  [  A  ]  chords  in  seven  meas- 
ures.    The  explanation  is  found  in  the  marking  under  the 
staff.     For  example,  [  A  ]  of  n  means  the  [  A  ]  chord  re- 
solving to  the  triad  on  the  second  degree  of  the  scale. 
Therefore,  after  the  [  A  ]  of  n  we  may  expect  to  hear  the 
chord  on  n.     In  the  second  measure  we  do  hear  it,  but  as 
it  has  a  major  3rd  D$,  it  becomes  also  the  [  A  ]  of  V, 
For  further  explanation  of  this  example  see    "  How  to 
Modulate,"  p.  7. 


1 68 


HARMONY  SIMPLIFIED. 


Fig.  80 


^ 

•    ^TTu  r 


IV 


HARMONY  SIMPLIFIED, 


169 


v7  v7 

273.  The  pupil  should  examine  some  of  Beethoven's 
Sonatas,  and  also  examples  from  Mendelssohn,  finding 
the  [  A  ]  chords  and  indicating  by  proper  marking  to  which 
degree  of  the  scale  they  are  attendant.     He  should  also  be 
on  the  alert  to  find  examples  of  [A]  chords  in  the  music 
in  daily  use. 

Exercises. 

274.  (a).     Write  little   successions  of  chords,  intro- 
ducing  one    or    two    [A]    chords.     Be    careful    not   to 
wander   away    from   the    key,   but   see    that   each   [A] 
chord  resolves  to  some  triad  in  the  key.     There  need  be 
but  three  or  four  chords,  after  which  a  close  may  be 
reached  by  a  Closing  cadence. 

(6.)  Repeat  the  above  at  the  keyboard.  (Continue 
this  keyboard  drill  indefinitely,  becoming  familiar  with 
all  keys.) 


170  HARMONY  SIMPLIFIED. 

275.  A  remarkable  feature  of  [A]  chords  is  that 
they  give  great  variety  by  enlarging  the  boundaries  of  the 
key,  so  to  speak,  instead  of  confining  everything  to  the 
chords  upon  the  seven  degrees  of  the  scale,  and  their  in- 
versions. 

Another  highly  practical  use  of  the  [  A  ]  chords  is 
their  wonderful  power  in  modulating.  This  will  be  ex- 
plained in  the  following  chapter. 

Synopsis. 
Form  as  usual. 


CHAPTER  XIII. 

MODULATION. 

276.  Modulation  is  the  passing  from  one  key  to 
«nother ;  and  is  effected  by  the  use  of  one  or  more  chords 
characteristic  of  (  belonging  to  )  the  key  to  -which  it  is 
desired  to  modulate. 

There  are  innumerable  ways  of  modulating,  but  the 
very  multiplicity  of  the  means  employed  has  always  made 
it  most  difficult  for  the  beginner  to  grasp  them,  and  the 
usual  result  is  utter  confusion  of  ideas,  and  little  practical 
skill  in  passing  from  key  to  key.  The  method  here 
presented  is  held  to  be  simple,  systematic,  and  compre- 
hensive. 

277*  Modulation  is  effected  by  connecting  some  chord 
of  the  "  old  key  "  with  some  chord  in  the  "new  key.'* 
(  N.  B."  Old  key  "  and  "  new  key  "  refer,  respectively,  to 
the  key  from  which,  and  the  key  to  which,  it  is  desired  to 
modulate. )  Therefore,  if  we  can  find  a  method  of  connect- 
ing any  two  triads,  the  difficulty  is  easily  solved. 


HARMONY  SIMPLIFIED. 


171 


Notice,  we  do  not  say  that  Modulation  is  effected  by 
connecting  the  "  old  "  Tonic  triad  with  the  "  new  "  Tonic 
triad ;  but  by  connecting  any  (  Major  or  Minor  )  triad  of 
the  "  old"  key  with  any  of  the  "  new"  key.  Our  range 
of  possibilities  in  variety  and  delicacy,  and  means  of  hid- 
ing the  modulation,  is  therefore  very  large  if  we  can  mas- 
ter this  one  point,  viz.,  to  connect  any  tivo  triads. 

To  Connect  any  Two  Triads. 

278.  It  has  been  shown  at  the  beginning  of  study  how 
chords  are  connected  by  means  of  a  common  note.  (  See 
§  102.)  We  have  also  studied  in  the  last  chapter  the  sys- 
tem of  Attendant  chords,  and  learned  that  any  Major  or 
Minor  triad  may  have  its  appropriate  [AJ  chord. 

Upon  trial  it  will  be  found  that  if  there  is  no  direct 
connection  between  two  given  chords  by  means  of  a  com- 
mon note,  the  connection  can  be  made  by  the  use  of  one 
or  both  of  their  Attendant  Chords.  Thus  it  becomes 
possible  to  connect  any  two  chords  without  considering 
whether  they  belong  to  the  same  key  or  to  different  keys. 

For  example,  let  us  connect  the  chord  of  C  with  the 
chord  of  FJJ.  As  there  is  no  common  note  to  connect 
the  two  triads,  we  will  write  them  with  their  Attendant 
chords,  which  we  will  indicate  by  [A], 

The  second  chord  in  Fig.  8 1  is  the  [A]  chord  of  C, 
the  third  chord  that  of  Ftf. 


Fig.  8 1 . 


[AJ  of  C.  [A]  of  Ft. 


172 


HARMONY  SIMPLIFIED. 


279.  Usually  only  one  [  A  ]  chord  is  necessary,  as  for 
example  in  connecting  the  triads  of  C  and  D  Major,  shown 
in  Fig.  82. 


Fig.  82. 


[A]  of  D. 


Thus  it  will  be  seen  that  although  two  chords  may 
not  have  a  common  note  to  connect  them,  when  we  con- 
sider their  Attendant  chords  a  connecting-link  will  become 
apparent. 

280.  In  the  following  exercises  the  pupil  will  connect 
two  given  Major  or  Minor  triads.*  The  mental  process, 
given  below,  will  be  of  much  assistance.  The  example 
given  to  illustrate  the  process  is  : — To  connect  the  triad  of 
C  major  with  the  triad  of  Bfr  major. — 

Process. 

NOTE.  Follow  this  process  with  the  hand  upon  the  keyboard, 
playing  each  chord  as  mentioned. 

Given,  to  connect  the  triad  of  C  with  that  of  £fy\ 
1st  Step.     What  are  the  [  A  ]  chords  of  the  triad 
from  which  and  the  triad  to  which  we  would  pass?** 
Ans.     The  [  A]  of  the  triad  on  C  is  G-B-D-F. 
The  [  A  ]  of  the  triad  on  Bt?  is  F-A-C-Eb. 
(Write  the  notes  for  reference) . 


*  Should  any  two  triads  have  a  common  note,  the  connection  may  be  made 
without  the  help  of  the  [  A  ]  chords.  But  in  many  cases  it  will  be  observed  that 
the  use  of  the  [  A  ]  chords  gives  a  smoother  connection  and  more  repose  when 
the  filial  chord  is  reached. 

*»  For  the  present  we  will  use  the  [  A  ]  chords  in  the  form  of  a  chord  of  the 
7th. 


HARMONY  SIMPLIFIED. 


'73 


2nd  Step.  Is  there  any  note  common  to  the  triad  of 
C  and  the  [  A  ]  of  Bt>. 

Ans.  Yes,  C  is  common  to  the  two  chords,  and  will 
enable  us  to  make  the  connection. 

3rd  Step.  Of  the  four  chords  before  us,  viz.,  the 
triad  on  C  and  its  [  A  ]  ;  and  the  triad  on  Bfr  and  its  [  A  ]  ; 
how  many  do  we  need  to  make  a  good  connection? 

Ans.  Three,  the  triad  on  C,  the  [A]  of  Bi?  and 
the  triad  on  Bfr. 

4th  Step.  Write  them,  trying  to  secure  a  good  lead- 
ing of  the  parts. 


Fig.  83. 


-fe- 


I 


fl 


C    [A]  of  Bb    Bb  C    [A]  of  Bb     Bb 

Could  this  connection  be  made  in  any  other  way? 

Ans.  Yes,  both  [A]  chords  could  be  used  instead 
of  one,  as  there  is  a  note  common  to  both  [  A  ]  chords. 
F  is  that  common  note. 

The  connection  using  both  [A]  chords  is  shown  in 
Fig.  84. 


Fig.  84. 


C  [A]  of  C  [A]  of  Bb  Bb     C  [A]  of  C  [A]  of  Bb   Bb 

Keyboard  and  Written  Exercises. 

N.  B.      While   working   out    these   exercises,    the   pupil   should 
constantly  refer  to  the  notes  in  §§  282-284. 


^^  i-— I  _          ^ 

-& &^      %.     .  z?H  — z? ttE, i 


'74 


HARMONY  SIMPLIFIED. 


28.1.  (  #•)  Connect  the  major  triad  on  C  with  the  majoi 
triad  on  C#. 

Connect  the  major  triad  on  C  with  the  major  triad 
onD. 

Connect  themajortriad  on  C  with  the  major  triad  on  DjJ. 
•Connect  the  major  triad  on  C  with  the  major  triad 
on  E. 

And  so  on,  till  the  triad  on  C  has  been  connected 
with  every  other  triad.  Then — 

( <5.)  Connect  the  triad  on  Qf  with  the  major  triad 
on  C. 

Connect  the  triad  on  C#  with  the  major  triad  on  D. 

Connect  the  triad  on  C$  with  the  major  triad  on  D#. 

And  continue  through  the  chromatic  scale  as  before. 

(c.)  Starting  from  the  triad  upon  each  remaining 
note  of  the  scale,  connect  with  every  other  triad. 

(a?.)  Connect  as  above  each  Minor  triad  with  all 
other  Minor  triads ;  and  with  all  Major  triads. 

282.  In  doing  the  above  exercises,  it  may  be  possible 
to  make  many  connections  in  two  or  more  ways,  viz., 

(a.)  Without  any  [  A  ]  chord. 

(  b.)  Using  the  [A]  chord  of  the  triad  to  which 
we  pass. 

(c.)  Using  the  [  A  ]  chord  of  the  triad  from  which 
we  pass. 

(  d.)  Using  both  [  A  ]  chords. 

N.  B.  The  Enharmonic  change  is  often  employed, 
changing  sharps  to  flats,  and  vice  versa. 

283.  If  only  one  [  A  ]  chord  is  used,  that  of  the  triad 
to  which  we  progress  will  usually  be  the  better  one,  for 
the  following  reason : 

The  natural  tendency  oi  an  [  A  ]   chord  is  strongly 


HARMONY  SIMPLIFIED. 


'75 


toward  its  triad,  like  the  tendency  of  a  Dominant  seventh- 
chord  towards  its  Tonic  triad.  Therefore,  in  connecting 
two  triads,  if  the  [A]  of  the  one  from  which  we  go  is 
used,  the  natural  tendency  would  be  to  return  to  that  triad ; 
whereas,  if  the  [  A  ]  of  the  triad  to  which  we  go  is  used, 
there  is  a  natural  tendency  to  continue  to  that  desired 
triad.  This  explains  why  some  of  the  connections  made 
by  the  pupil  wiH  be  harsh  and  forced.  (  The  next  para- 
graph will  show  how  the  above-mentioned  tendency  to 
return  may  be  hidden,  and  the  harshness  avoided.)  The 
difference  in  effect  between  the  [  A  ]  from  which,  and 
the  [  A  ]  to  which  we  go,  is  illustrated  in  Fig.  85. 

(a.)  W 


Fig.  85. 


[  A  ]  of  C.  [  A  ]  of  B. 

(  a  )  is  not  positively  bad  in  effect ;  but  the  superior- 
ity of  (  b  ) ,  using  the  [  A  ]  of  the  triad  to  which  we  pass, 
is  manifest  in  its  smoothness  and  repose. 

284.  To  remove  the  Tendency  to  return  shown  in 
the  [  A  ]  of  the  triad  from  "which  we  progress. — It  will 
be  found  that  by  inverting  this  [  A  ]  chord,  the  natural 
tendency  toward  its  triad  is  to  a  great  extent  hidden.  In 
composition,  chords  are  inverted  not  only  to  give  variety, 
but  also  to  induce  a  smoother  leading  of  the  individual 
parts.  Thus  the  melodic  tendencies  of  individual 
parts  become  more  prominent,  and  the  harmonic  ten- 
dencies less  so. 

From  this  we  learn  that : — 

(a.)  Inverting  an  [  A  ]  chord  reduces  the  force  of 
its  characteristic  tendency  toward  its  triad. 


!^6  HARMONY  SIMPLIFIED. 

1          (  6.)     Melodic  tendencies  of  the  individual  parts  also 
serve  to  cover  the  same  tendency. 

This  is  illustrated  in  Fig.  86,  where  the  same  con- 
nection as  in  (  a  ),  Fig.  85,  is  given,  using  the  [  A  ]  of 
the  triad  from  which  we  pass,  and  producing  a  very  sat- 
isfactory effect. 


Fig.  86. 


[  A  ]  of  C. 

Therefore : — In  using  the  [  A  ]  of  the  triad  from 
which  you  progress,  always  invert  it,  and  consider  the 
melodic  tendencies,  making  the  individual  parts  progress 
with  as  little  skipping  as  possible. 

To  Connect  any  Two  Keys. 

285.  Having   learned  to  connect  any  two  triads,  we 
proceed  to  connect  any  two  keys ;   for  it  is  evident,   that 
the  connection  (  or  modulation  )  is  effected  by  selecting 
a  triad  from  the  old  key  and  one  from  the  new  key,   and 
finding  the  connection  between  these  tivo  triads,  as  shown 
above.     And  when  the  two  triads  are  connected,  the  keys 
are   thereby  connected,   and  the  modulation  is  effected. 
Therefore,  the  connections  shown  in  Figures  81   to  86, 
might  be  taken  as  a  method  of  passing  from  one  key  to 
another,  instead  of  from  one  chord  to  another. 

Keyboard  and  Written  Exercises. 

286.  (  a.)      From  every  Major  key  modulate  to  every 
other  Major  and  every  Minor  key. 

(  3.)  From  every  Minor  key  modulate  to  every  other 
Minor  key  and  every  Major  key. 


HARMONY  SIMPLIFIED. 


177 


287.  Note  I.     It  should  be  observed  that  the  [  A  ]  chords  resolve 
equally  well  to  Major  and  Minor  triads.     Therefore,  the  Major  and 
Minor  triad  of  any  degree  ( for  example,  the  Major  triad  of  G  and  the 
Minor  triad  of  G  )  would  both  have  the  same  [  A  ]  chord. 

288.  Note  II.    Notice  that  the  [  A  ]  of  the  Tonic  chord  ( or  key ) 
to  which  we  modulate  is  nothing  more  or  less  than  the  chord  of  the 
Dominant  Seventh  resolving  to  its  Tonic. 

289.  Note  III.     To  thoroughly  establish  the  new  tonality  (or  con- 
sciousness of  the  new  key),  the  Closing  Formula  should  follow  the 
connection  of  the  two  triads,  particularly  if  the  triad  to  which  we  pr&- 
gress  appears  in  an  inversion.     The  sense  of  incompleteness  without 
the  Closing;  Formula  is  illustrated  in  the  following: 


F,g.87.^  -&&     I"-"** 


1 


r_z?_— ?± 


i 


6       W' 

IV    I*      V        I 

290.  In  the  preceding  pages,  we  have  learned  to  con- 
nect  any  two  triads,  and,  in  a  similar  way,  any  two  keys. 
The  process,  being  founded  upon  a  principle  which  is 
folloived  implicitly  in  all  cases,  might  be  represented  by 
a  formula  which  shall  give  a  visible  plan  of  procedure,  and 
show  between  which  chords  the  [  A  ]  chords  are  to  be  in- 
troduced, if  at  all.     The  chord-connections  shown  in  §§ 
278  to  288,  would  be  represented  by  the  formula : — 

Old  Chord,          [  A  ] ,        New  Chord. 
The  method  of  connecting  two  keys  by  connecting  the 
tonic  triad  of  the  old  key  with  the  tonic  triad  of  the  new 
key  would  be  : — 

_L_,        [A],  *     , 

Old  Key  New  Key 

291.  The  terms  Old  key,  and  New  key,    are  used  to 
indicate  briefly  that  the  chords  designated  by  the  Roman 


j^S  HARMONY  SIMPLIFIED. 

Numerals  belong  to  the  key  from  which,  or  the  key  to 
which,  we  modulate. 

The  Roman  Numerals  indicate  upon  which  degree 
of  the  scale  the  chord  (  a  common  triad  when  not  other- 
wise indicated  )  is  to  be  taken. 

[  A  ]  indicates  that  an  Attendant  chord  is  to  be  in- 
serted if  necessary.  Sometimes  two  [  A  ]  chords  may  be 
employed  to  advantage. 

292.  Observe  that  the  [  A  ]  of  _  is  simply  the 

New  Key 

chord  of  the  Dominant  Seventh  in  the  new  key. .  As  the 
progression  of  an  [  A  ]  to  its  triad  is  precisely  the  same 
as  that  of  a  Chord  of  the  Dominant  Seventh  to  its  Tonic 
triad,  we  may  draw  the  logical  conclusion  that  if  we 
can  pass  to  the  Tonic  of  a  Foreign  key  through  its 
Dominant  chord,  -we  can  pass  to  any  other  Major  or 
Minor  triad  of  a  foreign  key  by  using  Attendant 
chords. 

As  these  Attendant  chords  are  so  easily  found,  and 
have  a  most  intimate  relation  with  their  Primary  chords, 
they  will  prove  a  simple,  practical  and  correct  means  of 
connecting  the  original  key  with  any  desired  chord  of  the 
new  key. 

293.  With  the  assistance  of  the  Attendant  chords  it 
becomes  possible  to  formulate  the  principal  methods  of 
Modulation,  giving  a  most  thorough  and  comprehensive 
view  of  the  whole  subject. 

If  we  modulate  by  means  of  the  Dominant  Seventh- 
chord  of  the  new  key,  we  must  connect  the  original  key 
and  the  New  Dominant ;  if  we  modulate  through  some 
other  chord  of  the  new  key,  ive  must  connect  with 
that  chord.  Upon  this  plan  the  Formulas  are  con- 
structed. 


HARMONY  SIMPLIFIED. 


179 


Modulation  by  Means  of  the  Dominant  Seventh- 
Chord  of  the  New  Key. 

294.     According    to    the  heading  of  this  section,  we 

V7 

must  pass  through  __  ;     therefore,  the  first  prob- 

New  key 

I  V7 

lem  is  to  connect  __  and  _  .     Should  there 

Old  key  New  key 

be  a  note  common  to  both  chords,  we  can  proceed  at  once 
to  the  desired  chord.  If  not,  the  Principle  of  Attendant 
Chords  will  supply  the  connection.  Thus,  the  formula 

becomes  _          _,  [  A  ]   _ZIl*_  JL-     Observe  that  [  A  ] 

Old  key  New  key 

may  indicate  the  [  A  ]  chord  of  either  the  Old  Tonic  or 
the  New  Dominant,  or  of  both  if  necessary. 

To  illustrate,  let  us  modulate  from  C  to  F$. 


Now  the  formula  becomes  more  specific  : 


Old  key 

represents  the  triad  on  C  : represents  that  on  F#, 

New  key 

and  _____    _  the  Dominant  Seventh-chord  on  Qf.      As 

New  key 

there  is  no  connecting-note  between  the  chord  on  C  and 
that  on  CjJ,  we  resort  Lo  the  Attendant  Chords,  and  dis- 
cover that  we  can  use  either  the  Attendant  chord  of  C 
or  that  of  C#. 

Writing  the  chords  and  the  formula  together  shows 
plainly    the    connection,    using    first    the   [  A  ]   chord  of 

and  then  the  [  A  ]  chord  of ,    as  rep- 


Old  key  New  key 

resented  in  Figs.  88  and  89. 


•An  [  A  ]  chord  can  resolve  to  a  Seventh-chord  instead  of  to  a  simple  triad,  on 
the  ground  that  one  Dominant  Seventh-chord  can  resolve  to  another  (See  §  185.) 


i8o 


SIMPLIFIED. 


Fig.  88. 


Old  key       '    New  key 


Fig.  89. 


Old  key  New  key 

295.  In  every  case  of  Modulation  through  the  Dom- 
inant Seventh  of  the  new  key,  there  will  be  a  feeling  ot 
incompleteness.  This  will  disappear  if,  after  the  new 
Tonic  has  been  reached,  the  "Closing  Formula"  is 
added.  This  is  illustrated  in  Fig.  90,  where  the  same 
Modulation  as  in  Fig.  89  is  given,  with  a  slightly  differ- 
ent leading  of  the  parts  on  account  of  the  Closing  For- 
mula following. 


r.  00. 


Old  key        New  key 


Closing  Formula 


Keyboard  and  Written  Exercises. 

296.     For  the  first  exercises,  start  from  the  Tonic  triad 
of  C  and  pass  to  all  other  keys  through  the  new  Domi- 


HARMONY  SIMPLIFIED,  j.8i 

nant  Seventh-chord,  using  the  [  A  ]  chords  if  necessary 
to  make  the  connection.  Next,  proceed  from  Qf  to  every 
other  key ;  then  from  D  ;  and  so  on,  till  every  key  has  been 
used  as  a  starting-point  from  which  to  modulate  to  every 
other  key.  To  gain  the  fullest  benefit,  the  ^lupil  should 
practise  modulating  both  at  the  keyboard  and  in  writing. 

297.  Attention  must  be  paid  to  the  correct  leading 
of  the  parts.  A  Modulation  which  is  harsh  in  one  posi- 
tion and  with  a  certain  leading  of  the  parts,  may  often  be 
much  improved  and  softened  by  a  change  of  position  and 
different  movement  of  the  parts. 

It  will  be  found  that  while  many  of  these  Modula- 
tions are  harsh  in  spite  of  a  good  leading  of  the  parts, 
when  made  directly  through  the  new  Dominant  Seventh, 
they  may  be  made  very  pleasant  by  the  use  of  one  or 
both  [  A  ^chords.  The  student  must  not  fear  to  take  the 
chords  in  their  different  inversions  to  induce  a  smooth 
leading  of  the  parts. 

A  good  effect  depends  also  upon  a  proper  arrange- 
ment of  the  accents,  as  shown  in  §  190.  (  See  also  "How 
to  Modulate,"  §  15.) 

298.  When  we  use  the  [  A  ]  chord  of  the  new  Dominant,  we  touch 
the  key  of  the  Dominant  of  the  new  key,  as  we  make  use  of  the 
Seventh-chord  on  its  ( the  Dominant's  )  Fifth  degree.    Thus,  in  Fig.  89. 
the  new  key  is  FJ  and  the  key  of  its  Dominant  is  CJ.     Now  it  will  be 
seen  that  the  [  A  ]  chord,  having  Bf,  is  like  the  Dominant  Seventh- 
chord  in  the  key  of  C$.     Dr.  Stainer  says,  in  his  "  Composition,"  that 
a  new  key  should  be  entered  through  related  chords  or  related  keys. 
Here  it  is  plain  that  we  have  entered  through  a  related  key, —  that  of 
the  Dominant.     Thus  it  appears  how  the  System  of  Attendant  Chords 
fills  the  requirements  of  related  chords  or  related  keys  in  Modulation. 

Change  of  Mode. 

299.  The  change  from  a  Major  key  to  the  Minor  key 
of  like  name   (e.  g.,  C  Major  to   C  Minor)   cannot  be 


lS2  HARMONY  SIMPLIFIED, 

called  a  modulation,  since  the  key-note  is  not  changed,  but 
merely  the  mode.  Notice  that  the  chord  of  the  Dominant 
yth  is  the  same  in  both  Major  and  Minor,  and  that  the 
two  triads  may  follow  each  other  without  the  interposi- 
tion of  any  modulating  chord  (  Fig.  91,  a)  \  or  the  com- 
mon Dominant  yth  may  be  interposed  (Fig.  91,  6) . 
Many  examples  of  this  interchange  between  Major  and 
Minor  may  be  found  in  the  works  of  the  masters. 

(a.) 

C=BL 
Fig.  9  1 . 


300.  In  the  preceding  paragraphs  we  have  entered  the 
new  key  at  the  Tonic  triad  or  the  Chord  of  the  Dom- 
inant. It  is  equally  convenient  to  enter  at  any  other 
(Major  or  Minor)  triad  of  the  scale.  To  construct  the 
formula  for  such  a  case,  we  should  merely  substitute  the 

desired  degree  for  the  term . 

New  key 

It  is  also  possible  to  leave  the  "  old"  key  at  points 
other  than  the  Tonic  triad. 

The  [  A  ]  chords  can  be  used,  not  only  in  the  form 
of  seventh-chords,  but  also  in  the  form  of  Diminished 
yths,  Augmented  6ths,  or  Chords  of  the  9th.  These 
different  methods,  together  with  the  possible  diffeient 
points  of  leaving  the  old  and  entering  the  new  key,  offer 
great  variety  in  the  means  of  modulation.  The  chord  of 
the  Diminished  seventh  is  especially  useful  in  Modulation, 
since  it  has  a  direct  and  natural  resolution  to  four  differ- 
ent chords.  (  See  §  215.)  Having  just  seen  that  it  is  pos- 
sible to  enter  the  new  key  at  various  points,  each  one  of 
the  above-mentioned  chords  of  resolution  might  be  con- 
sidered either  the  Tonic,  Dominant  or  Supertpnic  of  a 


HARMONY  SIMPLIFIED.  ^3 

key.*  In  this  way,  each  one  of  the  four  chords  might  repre- 
sent not  one,  but  three  different  keys.  The  four  different 
chords  would  then  together  represent  twelve  different 
keys  ;  i.  e.,  all  the  different  keys.  It  is  therefore  possible 
to  modulate  from  any  chord  of  the  Diminished  seventh 
directly  into  any  one  of  the  twelve  Major  and  twelve 
Minor  keys. 

By  means  of  the  above-mentioned  methods,  it  is  pos- 
sible to  pass  directly  from  any  key  to  any  other.  This  is 
a  most  desirable  accomplishment  for  organists,  concert- 
players  and  accompanists,  who  are  frequently  called  upon 
to  bring  two  wholly  unrelated  keys  into  immediate  prox- 
imity in  successive  selections.  But  it  must  be  understood 
that  such  promiscuous  intermingling  of  keys  is  never 
allowed  in  constructing  any  single  piece  of  music.  In 
Composition  the  range  of  selection  is  usually  limited  to 
the  "Related  keys;"  viz.,  the  keys  of  the  Dominant, 
Subdominant,  and  their  Relative  Minors,  and  the  Rela- 
tive Minor  of  the  key  itself.  (  See  §§39  and  334.) 

Modulation  by  Means  of  a  Common  Triad. 

In  connecting  two  related  keys,  it  will  be  found  that 
instead  of  a  single  common  note  serving  as  a  connecting- 
link,  there  is  a  complete  chord  which  is  common  to  both 
keys,  offering  the  closest  possible  connection.  E.  g.,  in 
connecting  the  keys  of  C  and  G,  the  following  triads  will 
be  found  the  same  in  both  keys  :  — C  :  I  and  G  :  IV  ;  C  : 
in  and  G:  vi;  C:  vi  and  G:  n.  Any  one  of  these 
chords  may  be  used  as  the  connecting-link,  the  chord  be- 
ing approached  as  belonging  to  the  key  of  C  and  left 


*  Each  of  these  chords  could  just  as  well  be  taken  as  a  Mediant,  Subdomi- 
nant or  Submediant,  as  for  Supertonic  or  Dominant.  The  three  selected  are 
merely  more  prominent,  and  suffice  to  enable  one  to  modulate  to  all  keys. 


184 


HARMONY  SIMPLIFIED. 


as  belonging  to  the  key  of  G,  as  shown  in  the  marking 
under  the  illustration. 

(a.)  (b.)  (c.) 


— t^-l— L^J=  zt5 


V?     I 


(7:1 


in 
vi 


Keyboard  and  Written  Exercises. 

Starting  from  various  keys  in  turn,  modulate,  by 
means  of  a  common  triad,  to  each  of  the  related  keys,  as 
mentioned  above. 

There  are  also  many  other  ways  of  modulating,  which 
are  not  so  comprehensive  in  their  application  as  those 
already  described,  but  are  useful  where  circumstances 
happen  to  favor  their  introduction.  Being  of  good 
effect  and  in  common  use,  a  few  of  them  are  men- 
tioned :  —  (  a  )  Compound  modulation,  passing  through 
a  series  of  keys  to  the  one  desired  :  (  b  )  Single  Note  Con- 
nection ;  (  c  )  By  means  of  the  False  Cadence  ;  (  d  )  By 
means  of  Enharmonic  Change. 

All  the  above-named  means  of  modulation,  together 
with  the  principles  of  artistic  modulation,  are  described 
in  detail  in  the  author's  "  How  to  Modulate." 


Synopsis. 


Write  as  usual. 


UAttAIONY  SIMPLIFIED. 


185 


PART  III. 


CHAPTER  XIV. 

VARIETY  OF  STRUCTURE  :   SUSPENSIONS  :  ANTICIPATIONS  : 
RETARDATIONS. 

301 .  For  the  purpose  of  giving  variety  to  the  harmonic 
structure  of  a  composition,   many  devices  are  employed. 
Among  them  may  be  mentioned  Suspensions,  Anticipa- 
tions, Retardations,  Passing- Notes,    Passing-  Chords, 
Changing-Notes,  Appoggiaturas,  Organ-Points,   Sus- 
tained Notes,  and  Syncopations. 

These  devices  should  not  be  looked  upon  as  altering 
the  principles  of  chord-construction  already  learned,  but 
as  means  of  giving  greater  variety  to  a  Disposition. 
They  are  to  Musical  Composition  what  interior  decora- 
tion is  to  Architecture,  merely  a  means  of  ornamenting 
and  enriching  a  substantial  structure. 

Suspensions. 

302.  In  a  succession  of  chords,  when  one  tone  is  de- 
layed, or  held  over  till  after  the  next  chord  has  entered,  a 
dissonance  is  formed,  called  a  Suspension.     This  delayed 
and  therefore  dissonant  tone  moves  but  one  step  clown  or 
up,  usually  down,   to  its  tone  of  resolution  in  the  next 
chord. 


i86 


HARMONY  SIMPLIFIED. 


The  essential  features  of  a  suspension  are : —  the  Prep- 
aration, the  Dissonance,  and  the  Resolution.  The 
Preparation  consists  in  the  suspended  tone  being  pre- 
viously heard  as  an  essential  part  of  a  chord.  The  Disso- 
nance, technically  called  the  Percussion,  is  caused  by  the 
progression  of  a  single  part  being  delayed  while  the  remain- 
ing parts  proceed.  The  Resolution  is  effected  by  allow- 
ing the  delayed  tone  to  proceed  to  its  place  in  the  following 
chord.  In  Fig.  92,  the  Suspension  is  in  the  Alto ;  the 
first  note  is  the  preparation ;  the  second,  connected  with  the 
first  by  a  tie,  is  the  Dissonance,  or  Percussion ;  and  the 
third  note  the  note  of  Resolution. 


Fig.  92. 


I 


303.  Let  the  pupil  notice  the  following  conditions  im- 
plied by  the  definition  and  illustrated  in  Fig.  92  : — 

(a.)  One  note  is  held  over  and  prevented  from  pro- 
gressing with  the  others.  This  is  accomplished  by  the 
use  of  the  tie. 

(£.)  By  being  heard  in  the  first  chord,  the  sus- 
pended tone  is  prepared.  The  Preparation  should  be  as 
long  as  the  Dissonance,  else  the  Preparation  would  not  be 
sufficiently  marked. 

(  c.)  The  Preparation,  Dissonance,  and  Resolution 
should  be  in  the  same  part.  Otherwise  we  could  not  have 
(  particularly  in  vocal  music  )  any  effect  of  Preparation  or 
of  Resolution. 

( </.)     The  Suspension,  or   rather  the  Dissonance, 


HARMONY  SIMPLIFIED.  187 

should  be  heard  on  an  accented  part  of  the  measure.  A 
Dissonance  on  an  unaccented  part  of  a  measure  is  not  so 
prominent,  and  might  be  considered  as  a  passing  effect, 
i.  e.,  a  passing-note.  But  as  the  peculiar  effect  of  sus- 
pense is  desired,  it  is  necessary  to  bring  it  into  the  fore- 
ground by  placing  it  upon  a  prominent  (  accented  )  beat. 

(e.)  The  tone  that  is  delayed  should  not  be  heard 
meanwhile  in  another  part,  else  there  could  not  be  the 
effect  of  suspense  or  delay.  An  exception  to  this  is  when 
the  Bass  takes  the  note  of  resolution  at  a  distance  of  not 
less  than  an  octave  from  the  suspended  tone,  when  it  will 
not  be  disturbing. 

(y.)  The  purity  of  the  part- writing  must  not  be 
forgotten.  Suspensions  do  not  excuse  consecutive  5ths  or 
8ves,  though  one  part  may  be  delayed.* 

(,£".)  A  Dissonance  is  presupposed  in  a  Suspension. 
Therefore,  in  passages  where  the  delayed  tone  does  not 
create  a  dissonance,  there  is  not  technically  a  Suspension, 
though  it  is  treated  precisely  as  if  it  were. 

(  /*.)  The  suspended  tone  should  move  but  one 
step  to  its  tone  of  resolution.  Where  the  delayed  tone 
progresses  by  a  skip,  it  is  classed  among  Retardations. 
(See§  312.) 

Figuring  Suspensions. 

304.  Like  other  chords,   Suspensions  are  figured  by 
counting  from  the  Bass  note.     To  completely  express  a 
suspension  by  figures,  requires  that  both  the  dissonance  and 
the  resolution  be  figured. 

Exercises. 

305.  (  a.)     Turning  back  to  the  exercises  in  the  early 


*  It  is  held  by  some  writers  that  a  Suspension  does  cover  bad  progressions 
or  consecutives,  which  are  therefore  allowed  where  the  effect  is  good. 


i88 


HARMONY  SIMPLIFIED. 


pages  of  the  book,  the  pupil  may  try  to  introduce  Suspen- 
sions into  the  chord-connections,  trying  the  various  posi- 
tions and  deciding  which  are  practical.  It  will  be  found 
that  all  are  not  equally  effective. 

(  £.)  Write  examples  of  simple  chord-connections, 
and  try  to  introduce  Suspensions  into  all  the  different  parts. 
Write  in  various  keys. 

(c.)     Repeat  (<£.)  at  the  keyboard. 


3o6. 

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Exercises. 


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HARMONY  SIMPLIFIED. 


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307.  Suspensions  may  occur  in  two  or  more  parts  at 
once,  in  which  case  they  are  subject  to  the  same  rules  as 
when  occurring  in  only  one  part.  (Fig.  93,  a.) 

Suspensions  may  also  occur  with  a  progressing  Bass, 
i.  e.,  while  the  tone  of  resolution  is  sounding,  the  Bass 
progresses  to  another  tone,  thus  producing  a  new  chord- 
formation  (  Fig.  93,  <5),  or  another  inversion  of  the  same 
chord. 


Fig.  93. 


Suspensions  may  also  be  resolved  ornamentally,  i.  e., 
by  the  use  of  interpolated  notes  between  the  suspended 
note  and  its  resolution.  The  note  of  resolution  must  be 
the  same  as  if  no  ornaments  were  introduced  (  Fig.  93,  c). 


Exercises. 


190 


HARMONY  SIMPLIFIED. 


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HARMONY  SIMPLIFIED. 


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Anticipations. 

309.  In  a  Suspension  one  tone  of  a  chord  is  held  over 
till  after  the  next  chord  has  entered.  Anticipation  is  in 
one  sense  the  reverse  of  this,  for,  instead  of  being  delayed, 
a  tone  is  advanced,  or  heard  before  the  rest  of  the  chord. 
Differently  expressed,  it  is  where  a  tone  of  one  chord  is 
anticipated  in  the  previous  chord.  This  is  shown  by  the 
notes  marked  x  in  Fig.  94. 


.  94. , 


I 


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192 


HARMONY  SlMPLiFtts.0. 


310.  Notice  the  following  in  reference  to  the  above 
example : 

(  a. )  Unimportant  positions :  Suspensions  occur 
upon  the  accented  parts  of  a  measure ;  Anticipations, 
upon  unaccented  parts.  Anticipated  notes  are  also  usually 
short,  never  taking  more  than  half  the  value  of  the  pre- 
ceding note,  and  usually  less.  Anticipations,  therefore, 
are  seen  to  occupy  unimportant  positions,  in  respect  to 
both  rhythm  and  duration. 

(  £.)  Anticipations  are  usually  restruck,  i.  e.,  not 
tied  to  the  note  which  they  anticipate. 

(  c.)  Anticipations  do  not  need  to  be  prepared  and 
resolved  like  Suspensions.  They  may  enter  freely  by 
skips,  and  proceed  by  skips  if  desired. 


3"- 


Keyboard  and  Written  Exercises. 
Form  examples  of  Anticipations  in  various  keys. 


Retardations. 

312.  Retardations  are  the  opposite  of  Anticipations. 
A  tone  of  the  chord  is  held  over  while  the  remaining 
tones  progress  to  the  next  chord.  Retardations  differ 
from  Suspensions  in  being  treated  freely  like  Anticipa- 
tions; i.  e.,  they  require  no  preparation,  but  may  enter 
by  skips ;  and  (  b  )  they  are  allowed  to  progress  by  skips, 
not  being  forced,  like  Suspensions,  to  progress  to  the  note 
only  one  degree  higher  or  lower. 


Fig.  95.  < 


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0ARMONY  SIMPLIFIED 


'93 


Keyboard  and  Written  Exercises. 

313.  ( a.)     Form   examples  of  Retardations,  in  va- 
rious keys. 

(3.)     Form  examples,  mingling  Anticipations  and 
Retardations. 

Syncopation. 

314.  Syncopation    is    a    kind  of  irregular   Rhythm, 
where  the  more  important  notes  are  placed  upon  unimpor- 
tant beats  or  parts  of  beats ;  or  where  the  notes  fall  between 
the  beats.     It  may  be  produced  by  Anticipation  or  by  Re- 
tardation; i.  e.,by  pushing  forward  one  part  ahead  of  the 
others,    or  by  holding  it  back  till  the  others  have  moved. 
Fig.  95  is  an  example,  the  note  marked  x  serving  to  form 
a  Syncopation,  which  is  continued  by  the  retarded  notes 
marked  o. 


Synopsis. 


Write  as  usual. 


CHAPTER  XV. 

UNESSENTIAL    NOTES  :    PASSING-NOTES. 

Those  notes  which,   coming  after  a  chord,  ar*» 
not  essential  to  it,  but  lie  between  the  essential  noces,  are 

called  Passing-notes. 
(a.) 


Fig.  96. 


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'94 


HARMONY  SIMPLIFIED. 


Notice  the  following: — 

(  i.)  In  Fig.  96  the  notes  marked  x  do  not  belong 
to  the  chords. 

(2.)  These  marked  notes  serve  to  connect  the 
chord-notes  melodically  with  each  other.  In  Fig.  96, 
(  b  ) ,  the  chords  are  like  those  at  (  a  ) ,  but  in  (  a  )  the 
notes  marked  x  serve  to  lead  very  smoothly  from  one 
chord  to  the  next. 

(3.)  These  Passing-notes  may  occur  in  any  part. 
They  are  usually  found  upon  the  unaccented  portions  of 
the  measure,  when  they  are  called  Regular  Passing- 
notes  ;  but  are  occasionally  found  upon  the  accented  parts, 
when  they  are  called  Irregular  Passing-notes. 

(4.)  The  harmonic  structure  of  a  composition  is  of 
the  first  importance,  forming  the  basis  or  skeleton.  The 
passing-notes  and  other  ornaments  are  to  be  added  after- 
ward. 

316.  Passing-notes  may  be  chromatic  as  well  as  dia- 
tonic. In  Fig.  97  the  notes  marked  o  are  chromatic; 
those  marked  x  are  diatonic. 


Rff.  97. 


HARMONY  SIMPLIFIED. 


'95 


The  pupil  should  find  and  write  the  chords  forming 
the  harmonic  structure  of  Fig.  97,  as  at  (3),  Fig.  96. 

Care  must  be  exercised  in  securing  a  correct  leading 
of  the  parts  in  the  structure  of  the  harmonies,  i.  e.,  in  the 
chords  before  the  passing-notes  are  added,  since  concealed 
5ths  and  8ves  may,  by  the  use  of  Passing-notes,  become 
open  consecutives. 

Keyboard  and  Written  Exercises. 

317.  (a.)     Return  to  the  first  exercises,  Chapters  III 
and  IV,  and  insert  passing-notes  where  possible,  either  in 
the  given  Bass  or  in  the  upper  parts. 

(£.)     Try  this  exercise  at  the  keyboard. 

Exercises  in  Harmonizing  the  Scale. 
Harmonize  the  scale,  using  Passing-notes  where  pos- 
sible, together  with  the  chords  previously  learned. 

318.  Two  or  more  Passing-notes  may  be  used  simul- 
taneouslv,  or  even  all  the  notes  in  a  chord,  thus  forming 
a    Passing-chord.     Occurring  upon  unaccented  parts  of  a 
measure,  Passing-chords  are  not  expected  to  always  har- 
monize perfectly,  but  may  be  looked  upon  rather  as  a 
number  of  Passing-notes  leading  melodically  to  the  next 
chord  upon  an  accented  part  of  the  measure ;  for  upon 
the  principal  beats  the  harmony  should  be  quite  correct, 
thougrh  liberties  are  allowed  on  the  \veak  beats. 


Fig.  98. 


£96  HARMONY  SIMPLIFIED. 

319.      The  pupil  may  not  clearly  distinguish  between 
altered  chor.ds  and  chords  with  chromatic  passing-notes. 
The  following  constitutes  the  difference  : — 

(  i.)  To  be  an  Altered  chord,  the  tempo  should  be 
slow  enough,  and  the  accents  such  as  to  allow  the  al- 
tered note  to  be  heard  as  part  of  a  chord.  A  chromatic 
or  diatonic  scale-passage,  accompanied  by  a  single  chord, 
would  be  said  to  consist  principally  of  passing-notes ; 
e.  g-, 


(2.)  Only  chromatic  alterations  can  be  considered 
in  connection  with  altered  chords.  If  another  note  of  the 
scale  is  substituted  for  a  note  of  a  chord  (  making  a  dia- 
tonic instead  of  a  chromatic  change  ) ,  it  is,  of  course,  a 
passing-note.  A  note  may  be  said  to  belong  to  a  chord 
even  if  it  has  two  flats  or  sharps  before  it,  but  as  soon  as 
it  changes  its  name,  it  loses  its  membership  in  that  par- 
ticular chord;  e.  g.,  Fx  belongs  to  the  triad: 

but  if  we  call  it  G,  it  could  not  belong  to  the  triad  of  Dj. 

Auxiliary  Notes. 

320.  An  Auxiliary  note  is  one  used  for  ornament  or 
embellishment,  and  is  found  one  degree  above  or  below 
its  principal  note,  which  belongs  to  the  chord.  It  pre- 
cedes the  principal  note,  and  is  heard  either  with  or  be- 
fore the  remaining  notes  of  the  chord;  e.  g., 


HARMONY  SIMPLIFIED. 


197 


(S ,« —    — L.  -__. 


Fig.  100. 


The  peculiarity  of  the  Auxiliary  note  \$>,  that  while 
it  may  enter  by  a  skip  (i.e.,  need  not  be  prepared), 
it  must  progress  by  a  single  step  to  its  note  of  resolution. 
\  See  Fig.  100.)  These  notes  are  also  called  Changing - 
.votes,  Appoggiaturas,  and  Free  Suspensions. 

321.  Trills,  Shakes,  Turns  and  all  similar  ornaments 
are  classed  with  Auxiliary  notes.  This  principle  is  well 
expressed  in  "  Musical  Composition,"  Goetschius  (N.  Y., 
G.  Schirmer),  as  follows:  "Every  harmonic  interval  is 
attended  by  four  Neighboring  tones,  consisting  in  the  next 
higher  and  lower  Letters,  in  their  notation  as  whole  step 
and  half-step.  Thus: 


Fig.  101. 


^ 


I) 


The  Neighboring  tone  cannot  be  chromatic  (  as  at  Fig. 
01,  <5),  because  the  Letters  must  differ. 

"  The  Neighboring  tones  may  occur  in  almost  any 
connection  with  their  own  harmonic  interval  (  Principal 
tone  )  as  Unessential  or  Embellishing  notes. 

"All  the  common  forms  of  Embellishments  or  Grace- 
notes  (the  Turn, Trill,  Appoggiaturas,  Mordent,  etc.),  are 
based  upon  the  association  or  alternation  of  a  Principal 
tone  with  one  or  another  of  its  Neighboring  tones,  thus ; 


198 


HARMOATY  SIMPLIFIED. 


tr 


Fig.  102. 


"  o  signifies  '  Neighboring  note.'  " 

Keyboard  and  Written  Exercises. 
Construct  illustrations  of  the  above. 

Organ-Point. 

322.  An  Organ-Point,  or  Pedal-Point,  occurs  when  a 
note  in  the  Bass  is  sustained  through  a  succession  of  chords 
in  the  higher  parts,  part  of  which  chords  only  are  in 
harmony  with  the  Bass  note. 


Fig.  103. 


Notice  that  the  chords  marked  x  do  not  harmonize 
with  the  Bass,  but,  alternating  as  they  do  with  chords  of 
which  the  Bass  note  is  a  part,  the  effect  is  still  good. 

Essentials  of  Correct  Organ-Point. 

(a.)  The  first  and  last  of  the  series  of  chords  should  harmonize 
with  the  sustained  note. 

(6.)     The  first  chord  should  be  heard  upon  an  accented  beat. 

(c.)  Chords  harmonizing  with  the  sustained  note  should  pre- 
dominate, though  they  may  occupy  either  accented  or  unaccented 
beats. 

(</.)  As  a  rule,  the  Organ-Point  is  on  either  the  Tonic  or  the 
Dominant. 

The  lowest  part  above  the  Organ-Point  may  be  looked  upon  as 
forming  an  independent  Bass  for  the  upper  parts,  although  the  figur- 
ing is  reckoned  from  the  Organ-Point  if  that  is  the  lowest  note 
present. 


HARMONY  SIMPLIFIED. 


199 


Keyboard  and  Written  Exercises. 
Construct  illustrations  of  the  above,  and  also  of  the 
Inverted  Pedal.     (Next  paragraph.) 

Inverted  Pedal,  or  Sustained  Note. 

323.  When  a  sustained  note,  similar  to  the  above,  is 
found  in  one  of  the  upper  parts,  it  is  called  a  Sustained 
Note  (  or  Inverted  Pedal) .  Its  treatment  is  quite  similar 
to  that  of  the  Organ-Point. 


Fig.  104. 


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HARMONY  SIMPLIFIED. 


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General  Recapitulation. 

325.  ,  In  looking  back  over  the  last  two  chapters,  itwill 
be  seen  that  the  various  ornamental  devices  employed  pro- 
duce dissonances,  though  of  a  passing  or  transitory  na- 
ture. The  notes  which  produce  these  dissonances  do  not 
belong  to  the  chord,  i.e.,  they  are  not  Essential  notes. 

Comparing  these  notes  with  the  notes  which  produce 
the  dissonances  in  the  Chords  of  the  Seventh  and  other 


HARMONY  SIMPLIFIED.  2OI 

similar  chords,  we  find  that  in  the  latter  the  dissonant 
notes  belong  to  the  chord,  i.  e.,  they  are  essential  notes. 

Essential  notes  are  those  belonging  to  a  chord;  i.  e., 
not  transitory  or  ornamental. 

Unessential  notes  are  those  notes  used  with  a  chord, 
but  not  belonging  to  it.  Changing-notes,  Appoggia- 
turas,  Turns,  Trills,  and  other  ornaments  are  formed  by 
employing  Unessential  notes. 

This  leads  us  to  divide  Dissonances  into  two  classes : — 
those  produced  by  Essential  notes ;  and  those  produced  by 
Unessential  notes. 

Dissonances  formed  by  Essential  notes  are  called  Es- 
sential Dissonances. 

Dissonances  formed  by  Unessential  notes  are  called 
Unessential  Dissonances. 

Essential  Dissonances  may  be  further  divided  into 
Fundamental  dissonances,*  or  those  formed  like  Nature's 
Chord ;  and  Non-Fundamental  Dissonances,  or  those  not 
formed  like  Nature's  chord ;  e.  g.,  Secondary  Sevenths,  etc. 

Essential  Dissonances,  especially  the  Fundamental 
Dissonances,  resolve  naturally  according  to  the  Cadencing 
resolution. 

Unessential  Dissonances  are  free  in  their  resolution, 
or  are  controlled  by  the  Melodic  Tendencies  of  the  indi- 
vidual tones. 

The  pupil  is  now  prepared  to  understand  the  following. 

Division  of  Chords  into  Classes. 

326.       Chords   are   divided   into  Consonances,  or  Inde- 
pendent Chords,   and  Dissonances,  or  Dependent  Chords. 
Dissonances  are  divided  into  Essential  Dissonances, 
and  Unessential  Dissonances,  as  explained  above. 

Essential  Dissonances  are  divided  again  into  Funda- 
mental, and  Non-Fundamental  Dissonances. 


203 


HARMONY  SIMPLIFIED. 


The  above  might  be  shown  by  a  tabulated  synopsis. 

Con-     (  Major  Triads. 

sonan-  •< 

ccs.      (  Minor  Triads. 

•  Diminished  Triads. 

Dominant  seventh-chords 

Diminished  seventh- 

chords. 

Minor  ninth-chords. 

'Fun- 

Major  ninth-chords. 

da-    , 

Attendant  chords. 

men- 

(The   natural  resolution  of 

327-  . 

fa  i 

these  chords  is  to  the  triad  a 

Chords. 

till. 

4th  higher.     Occasionally  they 

progress  by  a  False  Cadence  to 

'Es- 

other  chords,  but  the  unnatural 

sen-  « 

effect  of  most  of  these  false  ca- 

frSol 

dences  only  serves  to  prove  the 

tiai. 

TVT 

^  principle.) 

JNlon- 

i        (  Secondary  seventh-  and 

,  1  ninth-chords.* 

Disso- 

men-  * 
tal. 

nan-     < 

kces. 

'  Altered  chords. 

Suspensions.** 

Passing-notes. 

CJn- 

Anticipations. 

es-   , 

Retardations. 

sen- 

Appoggiaturas. 

.tial. 

Trills,  Turns,  etc. 

(The  resolution  of  these  chords  de- 

pends upon  the  Melodic  Tendencies  of 

-  the  individual  tones.) 

*  It  is  scarcely  necessary  to  class  these  Secondary  chords  separately  from 
the  Fundamental  dissonances,  since  they  usually  resolve  in  the  same  way  to 
the  triad  a  4th  higher. 

**  Although  the  resolution  of  Suspensions  may  not  seem,  at  first  sight,  to 
be  dependent  upon  the  Melodic  tendencies  of  the  single  tones, yet  when  we  con- 
sider that  the  natural  tendency  of  one  tone  toward  its  place  in  the  next  chord 
has  been  checked,  and  brought  into  the  foreground,  it  is  clear  that  the  melodic 
tendency  is  even  stronger  than  in  other  cases. 


HARMONY  SIMPLIFIED  2O** 

From  the  above  it  is  clear  that  all  the  chords  used  in 
Music  may  be  divided  into  three  classes :  Consonances, 
Essential  Dissonances,  and  Unessential  Dissonances. 

The  Consonances  are  governed  by  the  simple  princi- 
ples of  chord-connection  and  part-leading ;  the  Essential 
Dissonances  are  governed  by  the  simple  principles  of  the 
Natural  Resolution  of  Dissonant  Intervals ;  and  the  Unes- 
sential Dissonances  are  governed  by  the  simple  principles 
of  Melodic  tendencies,  or  surrounding  circumstances. 

Synopsis. 
Write  as  usual. 


CHAPTER  XVI. 

MISCELLANEOUS  OBSERVATIONS  :  CROSS  RELATION :  THE 

TRITONE  :   THE  GREAT  STAFF  :    NAMING  THE  OCTAVES  : 

LICENSES:  SEOJJENCE. 

Cross  Relation, 

328.  Any  tone  in  a  chord  may  be  succeeded  in. the 
next  chord  by  the  same  tone  altered  by  an  accidental. 
But,  unless  the  same  part  takes  both  tones  (the  natural 
and  the  altered  ) ,  there  is  said  to  be  a  Cross  relation, 
often  producing  an  unpleasant  effect.  The  unpleasant 
effect  in  cross  relation  is  caused  by  the  fact  that  these  two 
tones  (  the  natural  and  the  altered  )  suggest  two  different 
keys  at  nearly  the  same  instant,  thus  producing  a  contra- 
diction. The  bad  effect  can  be  avoided  by  producing 
both  tones  in  the  same  part,  giving  the  effect  of  progres- 
sion rather  than  contradiction. 


HARMONY  SIMPLIFIED. 


Bad. 


Good. 


Pig.  105. 


The  above-mentioned  rule,  of  keeping  both  tones  ).a 
the  same  part,  might  well  be  counted  among  the  Influen- 
ces, since,  like  all  other  definite  rules  in  Harmony,  it  is 
occasionally  broken.  For  instance,  in  a  modulation, 
there  are  two  keys  in  close  succession,  and  thus  there  is 
no  contradiction. 

Even  where  there  is  no  modulation,  the  rule  is  some- 
times disregarded,  if  thereby  a  better  leading  of  the  part? 
can  be  secured.     Other  exceptions  allowed    are    Chra 
matic  passing-notes  (  since  the  structural  purity  is  not  af 
fected  )  ;    Appoggiaturas    (  for  the  same  reason  )  ;    and 
notes  which  are  variable,  as  the  6th  and  yth  degree  in  the 
Minor  scale.      (  See  Grove's  Dictionary,  Vol.  I,  p.  501.) 
These  (  apparent )  exceptions  are  allowed,  since  the  con- 
tradictory effect  is  less  marked  than  in  other  cases,  or  is 
entirely  absent. 

"NOTE.  When  the  note  to  be  chromatically  altered  is  doubled  in 
the  first  chord,  it  is  obvious  that  only  one  of  these  two  notes  should  be 
altered,  since  consecutive  8ves  would  occur  if  the  rule  were  applied  to 
both  notes  ;  e.  g., 


HARMONY  SIMPLIFIED.  205 

The  Tritone. 

329.  When    a   part  ascends  by  an  interval  of  three 
whole  steps,  it  makes  an  unmelodic  progression  called 
the  Tritone  (literally,  "three-tone").     This  can  occur 
only  in  passing  from  the  4th  to  the  yth  degree  of  the  scale 
(  unless  an  accidental  is  used  ) .     It  forms  an  interval  of 
an  augmented  4th.     The  upward  progression  of  any  aug- 
mented interval  is  rather  awkward,  and  this  is  particularly 
bad  because  the  Leading-tone    (  or   Sensitive  note,  as  the 
French  call  it  )   is  implicated.     Although  not  absolutely 
prohibited,  the  Tritone  should  not  be  used  without  some 
very  good  reason. 

The  Chord  of  the  Six-Four. 

330.  The  chord  of  the  f,  although  it  is  an  inversion  of 
the  independent  triad,  does  not  give  a  feeling  of  repose, 
especially   when   succeeding  a   dependent  chord;   e.  g., 


5^j,  but  seems  to  point  decidedly  toward  the 


end  of  a  musical  thought.  For  this  reason,  while  well 
adapted  to  introduce  a  Cadencing  Close,  it  should  be  used 
with  care  in  the  middle  of  a  phrase.  Under  the  condi- 
tions mentioned  below  it  does  not  point  so  clearly  to  a 
close,  and  therefore  may  be  used  at  any  time  : — 

(<z.)  In  connection  with  chords  on  the  same  Bass 
note;  e.  g.,  Fig.  106,  (a). 

(£.)  In  connection  with  chords  on  the  same  root; 
e  g...  Fig.  106,  (£). 

( c.)  In  connection  with  chords  on  neighboring 
Bass  notes;  e.  g.,  Fig.  106,  (c). 

(a?.)     When  it  is  a  Passing-chord;  e  g.,  Fig.  106, 


2O6 


HARMONY  SIMPLIFIED. 


Fig.  1O6. 


Licenses. 

Advanced  Course. 

331.  Liberties  are  sometimes  taken  with  the  interval  of  the  7th  in 
chords  of  the  seventh,  which,  though  considered  as  exceptions,  are 
rather  confirmations  than  contradictions  of  the  law  of  resolutions. 

There  are — 

( a.)  Delayed  resolutions  of  the  7th :  Where  one  or  more  chords 
are  interpolated  between  the  chord  of  the  seventh  and  its  resolution, 
in  which  interpolated  chords  the  dissonant  7th  appears  as  a  conso- 
nance. The  resolution  of  the  7th  must,  however,  ultimately  occur. 
E.g.,  Fig.  107,  (a): 

£: 


Fig.  1O7. 


( b.)  Transference  :  Where  the  dissonant  7th  is  transferred  t* 
another  part  and  there  resolved.  It  will  be  observed  that  the  resolu- 
tion still  takes  place,  though  in  another  part.  E.  g.,  Fig.  107,  (  b  ). 

Regular  Course. 

Sequences. 

332.  A  Sequence  is  a  repetition  of  a  progression. 
The  progression  ( i.  e.,  a  succession  of  two  or  more 
chords  )  is  repeated  in  gradually  ascending  or  descending 
succession;  e.  g., 


SIMPLIFIED. 


(a.)     (b.)    (a.)  (5.)     (a.)  (6.)     (a.)  (6.) 


— x^ — ^. — — C*3 jz, — L  S xa — 1~^ <SJl_. 


pier.  los. 


In  this  example,  the  Bass  alternately  descends  a  4th 
and  ascends  a  2nd. 

To  harmonize  a  Sequence,  the  parts  should  move 
go  that  the  Sequence  may  be  preserved  in  the  chords  and 
in  the  movement  of  all  the  parts.  Thus,  if  in  the  first 
or  "  pattern  "-progression  the  Soprano  of  the  first  chord 
is  (for  example  )  a  loth  from  the  Bass  (  see  #,  Fig  108), 
the  interval  of  a  loth  should  be  found  in  the  ist  chord  ot 
each  following  progression.  (  See  #,  <z,  <z,  a,  Fig.  108.) 
Furthermore,  if  in  the  pattern-progression  the  Soprano 
should  progress  one  degree  downward  to  its  place  in  the 
second  chord,  the  same  movement  should  be  found  at 
the  corresponding  place  in  the  following  progressions. 
(See  3,  <5,  3,  Fig.  108.) 

To  carry  out  a  Sequence  exactly,  it  is  frequently  ne- 
cessary to  take  liberties  with  the  rules  of  part-leading,  ten- 
dencies, doubling,  and  especially  the  rule  regarding  the 
common  connecting-note  for  two  successive  chords  re- 
maining in  the  same  part. 

Sequences  may  occur  in  progressions  of  triads,  of  chords 
of  the  seventh,  or  of  suspensions.  They  may  also  consist 
of  the  repetition  of  a  series  of  two,  three,  or  more  chords. 


R. 


Exercises. 


i 


a.      - 


N.  B. 

G> rf2 


I~~^T — — -i  ex 1- 1— 

^S> -P*— ^5-  -I SH-H 

EBSiSyEi 


6. 


Emery. 


p~7-rF 

S3 

'   " 

3^ 

"3 

"11 

cz  ID 

1 

(^ 

S>__ 

—  J 

II 

Y^     Em 

ery. 

1 

6 
4           7 

i  Q^ 

, 

(*? 

i"        ri 

L-Ji/* 

^d 

a 

r^^/ 

S. 

•  ^         3ZJ 

i         fi' 

1 

^    II 

N.  B.     The  Tritone  is  here  allowed,  for  otherwise 
the  sequence  would  be  broken. 

Advanced  Course.        [Quoted  from  Banister's  "  Music."] 

333.  "A  Sequence  is  termed  Real  when  all  the  chords,  or  intervals, 
are  major,  minor,  etc.,  at  each  recurrence  of  the  pattern-progression  as 
at  the  original  occurrence  of  it. 

"A  Sequence  is  termed  Tonal  when  the  chord  or  intervals,  at  each 
recurrence,  are  according  to  the  key  in  which  the  passage  occurs,  and 
therefore  do  not  strictly  resemble  the  original  pattern.  This  is  the 
more  frequent  kind  of  sequence.  Fig.  109  is  a  Tonal  sequence  ;  two 
of  the  ascending  2nds  are  major,  one  (from  D  to  Eb)  minor;  more- 
over, some  of  the  chords  are  major,  others  minor. 

"The  preservation  of  a  sequential  progression,  will  often  lead  to 
and  justify  exceptional  intervals,  doublings,  etc.;  the  symmetry  of  the 
sequence  outweighing  the  objections  which  might  otherwise  lie  against 
such  exceptional  arrangements.  Design,  using  the  word  in  its  artistic 
sense  of  intelligent  aim  at  a  defined  and  desirable  effect,  especially 
with  regard  to  form,  reconciles  and  more  than  reconciles  the  mind  to 


HARMONY  SIMPLIFIED. 


209 


details  which,  taken  by  themselves,  would  be  questionable  or  even 
positively  objectionable. 

"In  Fig.  no,  for  example,  the  Tritone  4th  in  the  Bass,  from  C  to 
FJ,  and  the  non-resolution  of  the  Diminished  5th  in  the  Tenor,  at  *, 
till  the  next  chord  but  one,  are  both  justified  by  the  sequential  form 
of  the  passage. 

"  Such    exceptional   progressions,  however,  though  permissible 


BANISTER. 


Fig.  109. 


J  L_U  L 

in  the  course  of  the  sequence,  must  not  occur  in  the  original  pattern, 
in  which  the  writing  must  be  perfectly  pure." 

BANISTER. 


Fig.  1  1  O. 


rz?-gq_gj_^!ipi^:p 


Related  Keys. 

334.  In  §  32  the  keys  related  to  a  given  key  were 
stated  to  be  the  key  having  one  more  sharp  (  its  Domi- 
nant ) ,  and  the  key  having  one  less  (  the  Subdominant  ) . 
To  these  may  be  added  the  Relative  Minors  of  the  key 
itself,  of  its  Dominant,  and  of  its  Subdominant.  Thus 
the  relative  keys  of  the  key  of  C  are :  the  key  of  G  (  the 
Dominant  ) ,  the  key  of  F  (  the  Subdominant ) ;  the  key 
of  A  minor  (  Relative  Minor  of  C  ) ,  the  key  of  E  minor 


2IO 


HAxMONY  SIMPLIFIED. 


(Relative  Minor  of  G),  and  D  minor  (Relative  Minor 
of  F).  To  this  may  be  added,  as  it  is  so  frequently 
used — though  not  allowed  by  all  theorists — the  Tonic 
Minor,  or  Minor  key  of  the  same  name,  in  this  case  C 
minor. 

The  related  keys  of  a  Minor  key  are  the  Minor  keys 
of  its  Dominant  and  Subdominant,  and  the  relative 
Majors  of  all  three,  i.  e.,  of  the  key  itself,  of  its  Domi- 
nant, and  of  its  Subdominant,  to  which  we  may  also  add, 
as  above,  the  Tonic  Major.  Thus,  the  related  keys  of 
C  minor  are  G  minor  and  F  minor,  Eb  major,  Bb  major, 
Ab  major  and  C  major. 

Naming  the  Octaves. 

335.  Musicians  speak  of  Three-lined  A,  Great-octave 
B,  Small-octave  F,  etc.  The  system  of  naming  the  vari- 
ous octaves  is  as  follows : — 

This  note  and  the 
six  notes  below  are 

called  the  Sub-  Contra-  Great  Small 

Octave.  Octave.  Octave.  Octave. 


Marked  j^ 

Once-accented 
or  One-lined 
Octave. 

C  

Twice-ac- 
cented, or 
Two-lined 
Octave. 

B_ 

Three- 
lined 
Octave. 

***» 

JSl-     ^ 
-*L_L  

Four-lined 
Octave. 
8va  M 

Marked  c 

b"       c 

\.  

K     c 

be"               T> 

(  d 

hi        C2 

b3    c3 

b»   c*             b* 

or:|e, 

h'      c" 

b"   C'" 

^rrr^tftr               \/ffi- 

SIMPLIFIED.  211 

The  Great  Staff:  the  C  Clefs. 

336.  In  very  old  music,  instead  of  two  staves  of  five 
lines  each  and  an  added  line  above  the  Bass  or  below  the 
Treble  for  middle  C,  a  great  staff  of  eleven  lines  was 
used ;  and  the  various  parts,  Bass,  Tenor,  Alto,  and  So- 
prano, were  placed  high  or  low  upon  this  staff,  accord- 
ing to  the  pitch  of  the  voice : 

Fig.  111. 


The  notes  in  the  great  staff  were  written  just  as  in 
the  present  system,  G  being  the  lowest  note  in  the  Bass, 
and  leading  up  step  by  step  to  the  5th  treble  line,  which 
is  F.  Notice  that  the  6th  line  is  C,  corresponding  to  our 
middle  C.  In  fact,  our  staff  is  the  same  as  the  old  one, 
except  that  to  help  the  eye  the  middle  Iin2  is  omitted  un- 
less actually  in  use,  when  it  is  written  as  an  added  line, 
and  the  two  sections  are  separated  a  little. 

The  sign  ISt  is  called  the    C  clef,  and  always  de- 

-f^H~  * 

notes  middle  C,  or  the  6th  line  of  the  great  staff.  In 
forming  a  Tenor  staff,  for  example,  it  is  considered  in 
which  part  of  the  great  staff  the  chief  notes  of  the  Tenor 
'lie  (all  staves  consisting  of  five  lines  and  four  spaces  ) . 
^ow,  the  Tenor  sings  most  easily  from  the  3rd  line  of 
iie  great  staff  to  the  seventh  line,  or  from  small  D  to 
jne-lined  E.  It  not  being  necessary  to  employ  all  of 
the  Great  staff  for  the  limited  compass  of  the  Tenor,  it 
became  customary  to  take  out  the  proper  section  of  the 
great  staff,  leaving  the  clef  to  denote  which  part  had  been 
taken.  Reference  to  Fig.  us,  (a),  and  112,  (<£),  will 


212  HARMONY  SIMPLIFIED. 

make  it  clear  how  the  Tenor,  Alto  and  Soprano  staves 
were  formed. 

The  C  clef,  then,  instead  of  moving  about  for  the 
different  staves,  in  reality  remains  stationary,  different 
parts  of  the  great  staff  being  used  with  it  to  suit  the  com- 
pass of  the  different  voices. 

Fig.  112,    a.  Treble 

or 

Tenor   Alto      Sop.  Violin 

Tenor.  Alto.     Sop.  Clef.      Clef.       Clef.  Clef. 


Middle  TT—  I    I        I  4=  Middle  4H-H.       T^T;       ^rr 

^EB— c-    ]Ui    flE    iflf   c  •"-  - 


c.- 


Flg.  112,    ( 6.) 

Tenor.  Alto.      Sop.        Treble. 


Middle  C. 


c- v1-  - 

Exercises. 

These  clefs  should  be  brought  into  use,  either  by 
writing  future  exercises  in  them,  or  by  copying  past  exer- 
cises, hymn-tunes,  etc.,  employing  a  separate  staff  for 
each  part,  thus  forming  what  is  called  Vocal  Score. 

Chords  of  the  Eleventh  and  of  the  Thirteenth. 

337.  According  to  the  principle  of  forming  chords  by 
tae  addition  of  a  note  a  3rd  above  the  last  note,  we  may 
form  chords  of  the  nth  by  the  addition  of  a  note  to  the 


Chord  of  the  9th;  e.  g., 


5!" —  ;  and  if  to  this  Chord  of 


the  nth  we  add  still  another  3rd,  we  shall  have  a  Chord 
of  the  i3th;  e.  g., 


HARMONY  SIMPLIFIED.  2 1 3 

These  chords  have  no  practical  application  in  Har- 
mony, since  so  many  notes  must  be  omitted  in  four-part 
writing,  and  the  dissonant  intervals  prepared,  that  they 
become  practically  nothing  more  than  suspensions. 

Exercises  in  Open  Position,  or  Dispersed 
Harmony. 

338.  The  pupil   is   now    sufficiently   experienced    to 
write  in  Open  position,  placing  the  Tenor  part  upon  the 
Bass  staff.     It  is  not  required  that  every  chord  shall  be  in 
open  position ;  when  more  convenient,  close  position  may 
be  used. 

In  distributing  the  parts,  try  to  keep  the  larger  inter- 
vals between  the  lower  parts.  Avoid,  if  possible,  hav- 
ing more  than  an  octave  between  the  Tenor  and  Alto,  or 
between  the  Alto  and  Soprano. 

Exercises. 

Refer  to  the  exercises  in  the  preceding  chapters,  and, 
ignoring  the  figure  over  the  first  Bass  note  (  i.  e.,  trying 
various  positions  ) ,  write  them  in  Open  position.  The 
results  will  not  always  be  satisfactory,  but  the  comparison 
of  the  effect  in  the  various  positions  will  be  helpful. 

Five,  Six,  Seven,  and  Eight-Part  Harmony. 

339.  Having  studied  the  principles  of  Harmony  rather 
than  a  series  of  set  rules,  the  pupil  will  be  able  to  write  in 
more  than  four  parts,  without  special  directions.    The  Ten- 
dencies and  Influences  will  need  to  be  interpreted  with 
rather  more  freedom,  on  account  of  the  increased  compli- 
cation resulting  from  the  larger  number  of  parts. 

Exercises. 

The  pupil  will  attempt  to  compose  phrases  of  eight 
measures,  introducing  five,  six,  seven  or  eight  parts. 


214 


HARMONY  SIMPLIFIED. 


CHAPTER  XVII. 

HARMONIZING    MELODIES. 

340.  The  pupil  has  learned  to  build  chords  upon  a  given 
Bass,  and  to  connect  them.  It  is  now  necessary  to  find 
appropriate  harmonies  for  a  given  melody,  or  to  supply 
the  remaining  parts  for  a  given  Tenor  or  Alto.  Hitherto 
the  chords  have  been  chosen  for  the  pupil ;  now  he  must 
choose  them  for  himself.  Especial  care  is  required  in 
this,  one  of  the  practical  applications  of  the  previous  study. 
The  pupil  has  used  chords  in  their  various  inver- 
sions. He  has  also  learned  that  any  particular  note  may 
belong  to  several  chords,  a  fact  which  renders  the  first 
attempts  somewhat  confusing.  For  example,  the  note  C 
may  belong  to  any  one  of  the  following  chords : — C— E— G, 
F-A-C,  A-C-E,  D-F-A-C,  or  F-A-C-E,  all  of  which 
are  strictly  in  the  key  of  C,  besides  the  list  of  altered, 
diminished,  and  [A]  chords.  The  best  harmony  for  a 
given  note  will  depend  principally  upon  the  chords  pre- 
ceding and  following.  In  the  exercises  below,  the  appro- 
priate harmony  will  be  indicated. 


Exercises. 

1. 

C         G          C                      F          d7 

\_yr»                         (_, 

h? 

V  ,K 

^j 

™ 

^S 

•5 

e       i 

L    /*       ** 

r 

S3E 

i 

d7 


HARMONY  SIMPLIFIED.  215 

2      J.        F         Bb        F         Bb        C7        Bb         C7          F 


g  F  §7  F  g7 


:fe&_^ 

* 

1  —  «•  — 

0 

g    1  ~fc» 

g  H 

F,          Bb          Eb          Bb  CT          F^ 


-ifc*   ^7- 

" 

•   ^ 

I.C)      V"  \  1 

r 

TBZS—Z. 

Of 

<y 

<?      11 

tax* 

i^> 

:  * 

4. 


D7  G  a,  D7  G  D 


XI    "  /'I*       n 

°~^ 

& 

<5 

i?t\  \  /    z 

& 

f3 

G  C  D7         G  e  a7          D7          G 


J.          Eb    Ab    Eb    c    Ab    Bb    c7     f7     Eb    £7      Bb  Eb 


/Lb  K/4   n 

<2 

^^ 

ri 

^^ 

^.^^^^ 

tf<\9  v\\j  & 

t* 

^ 

^ 

& 

-5 

J.  Gb       Db        eb        bb         eb       Db        D^       Gb 


Zjaanz3 

S3 

fmpi?fi  v 

y 

^ 

Gb        eb         4        D7        Gb 


1 


2l6 


HARMONY  SIMPLIFIED. 
A  E  A  D  A 


m 


r-<5>- 


m 


E7       f7         b-y         E^ 


341 .  In  the  following  exerctees,  the  melody  to  be  har- 
monized ( also  called  the  Cantus  Firmus  )  is  placed  in 
the  Alto,  the  parts  to  be  supplied  being  the  Soprano, 
Tenor  and  Bass.  Write  the  exercises  in  Open  position. 


J.      C 
1.  ^J 


G7 


\f> 


F7T- 

s? 

Efc: 

ey 

& 

—  &  — 

B 

2. 


J.      F      C7    F     g7    C7    F, 


«    F       g      F      C       F 


%Fg-| 


& 


d      g      e°    A7   d      g       A7    Bb     g      A7    d 


In  the  next  exercise,  the   Cantus  Firmus  is  in  the 
Tenor.     Supply  the  other  parts,  writing  in  Open  position. 
P         Eb         Ab        Bfc          Eb         Ab 


Eb 

-G>- 


I 


HARMONY  SIMPLIFIED. 
f7          B£  Eb         f7          Eb         f7 


217 


E 


•l',V 

g  f  JO  g  C 

2J-  /^  "^"  <7_  -a. 

•  CJr* 


D7 


f^'     U     i 

E 

L^ 

--^—^y  (]*  — 

*/    * 

g           a°          g            D           Eb         a°         D7         g 

-<s>- 

a 

:Bi;i2= 

Zffi± 

d      A7  d       A      d     g      A7     d      cto  d      e°    A     d 

^-  -Or-      5tf?~      -"^-    -»-*-    5^"       *"•    — *  •"" 


—  H 

g    D7   Eb   a°   g 

J'         -<2.   _«- 


§    g      a<>    Eb    a°     g      D       g 


342.  In  the  following  exercises,  in  which  no  assis- 
tance is  given,  the  pupil  should  endeavor  to  find  chords 
which  progress  smoothly  from  one  to  another,  constantly 
looking  ahead  to  see  if  the  following  chord  will  easily 
succeed  the  one  under  consideration.  The  following 
hints  will  be  found  helpful : — 

(i.)  Use  simple  harmonies.  Do  not  attempt  to 
be  original  at  first,  but  be  content  with  commonplace 
effects. 

(2.)  The  Principal  triads  are  used  more  than  the 
others,  but  the  Secondary  triads  should  not  be  neglected. 

(3.)  Inversions  are  conducive  to  smooth  progres- 
sions. 


218 


HARMONY  SIMPLIFIED. 


(4.)  Contrary  motion  is  like  oil, —  it  helps  the 
smooth  running  of  the  parts. 

(  5«)     Do  not  let  too  many  parts  skip  at  one  time. 

(  6.)  Avoid  consecutives  : — not  only  5ths  and  8ves, 
but  also  4ths,  2nds  and  7ths. 

(7.)  Keep  the  parts  at  about  an  equal  distance 
from  each  other. 

(  8.)  Do  not  let  any  part  exceed  the  limits  of  a  good 
voice  of  corresponding  pitch. 

(9.)  Use  the  2  chord  in  the  middle  of  an  exercise 
with  caution.  This  chord  usually  indicates  a  close  too 
keenly  for  use  except  in  a  cadence,  or  under  special  con- 
ditions. 

(10.)  Secondary  chords  of  the  seventh  resolve, 
like  the  chord  of  the  dominant,  most  naturally  to  the  triad 
a  4th  higher. 

(  n.)  Apply  the  principles  of  Influences  and  Ten- 
dencies. 

(  12.)  When  the  Soprano  is  low,  the  chords  should 
be  in  close  position.  With  a  high  Soprano,  the  chords 
should  be  in  open  position. 


Exercises. 


Dr.  CROFT. 


WARSAW.    L.  M. 


HARMONY  SIMPLIFIED. 


219 


Other  chorals  and  slow  hymn-tunes  should  be  se- 
lected and  used  as  melodies  for  harmonization.     They 
may  be  used  in  the  Alto  or  Tenor  as  a  Cantus  Firmus, 
when  transposed  to  a  key  suited  to  the  voice  taking  them. 
Observe  the  Soprano  Clef  below.     See  p.  212. 


ggapnirs 

Q        -^                   '- 

ex 

1 

ifli 
j»  *  ....                  & 

^—  *^ 

i               Jr    * 

^     '    •^ 

j*b                X^3 

/rj 

& 

&^             &^ 

*   fl 

& 

^^ 

<V            X3 

"A,  I) 

••^ 

cs 

~^ 

1 

y 

t 

\ 

M 

Tfr 

J. 


3. 


J- 


•543.  An  interesting  form  of  exercise  in  harmonizing 
.•nelodies  is  the  Chant.  Being  one  of  the  shorter  forms,  it 
will  be  easy  for  the  pupil  to  compose  little  melodies  in 
the  form  of  a  chant,  and  then  add  the  other  parts  as  in 
the  previous  exercises. 

The  chant  in  its  simplest  form  consists  of  four  parts: 
(  i  )  The  first  Reciting-note ;  ( 2  )  A  short  Cadence  of 
two  measures  5(3)  The  second  Reciting-note ;  (  4  )  A 
fuller  Cadence  of  three  measures. 


220  HARMONY  SIMPLIFIED. 

The  Reciting-notes,  or  Recitatives,  are  so  named  be- 
cause they  have  no  definite  duration,  but  must  be  held  till 
a  certain  number  of  syllables,  sometimes  few  and  some- 
times many,  have  been  sung. 

The  first  cadence  is  called  the  Mediation.  The  sec- 
ond cadence  is  called  the  Cadence. 

There  should  be  no  mark  of  rhythm  in  a  chant, 
owing  to  the  variations  in  the  length  of  the  recitative. 
Both  the  Mediation  and  the  Cadence  should  be  in  strict 
time,  however. 


Fig.  1  13. 

Reciting-note.  Mediation.   Reciting-note.  Cadence. 

A  Double  chant  is,  in  form,  like  two  single  chants  ir 
succession,  with  suitable  harmonic  connection. 

Exercises. 

Form  the  melodies  of  single  chants,  and  harmonize 
them. 

NOTE  I.  It  is  still  better  to  think  both  the  melody  and  its  ap- 
propriate harmony  together,  as  all  musicians  do,  on  account  of  the  har- 
monic connections,  or  the  relations  of  the  chords  to  each  other. 

NOTE  II.     (  From  Banister's  "  Music.") 

344.  "  In  commencing  an  exercise  in  which  the  melody  is  not  given, 
observe  the  early  progression  of  the  Bass.  If  it  ascends,  be  care- 
ful not  to  begin  with  the  parts  so  near  to  it  as  to  force  too  much 
similar  motion.  If,  on  the  other  hand,  the  Bass  descends,  begin  suf- 
ficiently near  it  to  prevent  the  parts  becoming  too  much  separated 
from  it. 

"  In  all  cases,  throughout  the  exercises,  look  forward,  endeavor- 
ing to  trace  the  consequences  of  each  position  and  progression,  as 
much  as  possible." 

The  above,  with  slight  modification  of  the  terms  to  make  it  gen- 
erally  applicable,  forms  excellent  advice  for  this  period,  when  the  pupil 
makes  his  first  attempts  in  independent  writing. 


SIMPLIFIED.  221 

345.  If  the  pupil  can  now  compose  little  melodies  of 
four  or  eight,  measures,  hymn-tunes,  or  chants,  it  will  be 
of  great  assistance.     As  he  will  need  help  in  regard  to 
the  formation  of  phrases,  periods,   sections,   whole  and 
half-cadences,  etc.,  it  is  well  to  take  some  standard  hymn- 
tune  or  short  melody,  and  carefully  analyze  it,  to  find  the 
number  of  measures  in  each  phrase,  and  trace  the  caden- 
ces and  modulations ;  then  try  to  form  a  new  melody  after 
the  pattern  of  the  model. 

To  Acquire  Speed  In  Writing. 

346.  In  order  to  gain  facility  and  ease  of  expression, 
it  is  well  to  apply  speed-tests  in  writing  exercises.     To  do 
this,  review  the  exercises  in  the  earlier  chapters,  allowing 
the  shortest  possible  time  for  each  exercise. 

Practical  Application  of  Studies  in  Harmony. 

347.  The  true  student  will  not  fail  to  make  practical 
application  of  all  the  subjects  developed  in  the  pages  of 
this  book.     The  exercises  are  designed  to  cultivate  not 
merely  a  theoretical  but  a  practical  working  knowledge 
of  the  chords.     But  in  regard  to  proficiency  in  Modulat- 
ing, in  the  use  of  Sequences,  Passing  and  Changing-notes, 
Suspensions,  Anticipations,  Retardations  and  Attendant 
chords,  while  instruction  must  lead,  it  cannot  do  the  work. 
Every  one  must  strive  for  himself,  not  only  to  understand 
these  things,  but  to  introduce  them  into  his  productions. 
He  should  be  able  to  modulate  correctly  and  without  hesi- 
tation, and  to  introduce  suspensions,  passing-notes,  sequen- 
*es,  etc.,  into  his  improvisations  in  a  natural  and  finished 
manner.     This  proficiency  is  indispensable  for  composers 
and  organists,   and   is  necessary  for  all  who  would  have 
a  broad  and  thorough  knowledge  of  Music. 

For  this  reason,  the  course  in  Harmony  should  not 


222  HARMONY  SIMPLIFIED. 

be  considered  completed  until  several  months  have  been 
Jevoted  to  the  study  of  the  subjects  here  mentioned,  and 
the  power  of  easy  manipulation  gained.  It  is  not  suffi- 
cient to  know  about  these  things;  we  must  do  them. 

.  To  gain  this  proficiency,  the  pupil  must  work  for 
himself,  under  the  eye  of  the  teacher.  Exercises  cannot 
be  given,  as  everything  must  be  evolved  from  the  brain 
of  the  pupil  if  he  would  gain  complete  independence. 
But  the  following  is  given  to  secure  systematic  application. 

Order  of  Study. 

348.  A  practical  order  of  study  in  undertaking  the 
above  will  be:  — 

Freedom  in  the  use  of  the  following ;  (  i  )  Second- 
ary Triads  in  Major  :  (  2  )  Secondary  Triads  in  Minor  : 

(3  )  Secondary  Chords  of  the  yth,  including  the  Prepa- 
ration of  the  dissonant  notes :  (  4 )  Chords  of  the  9th, 
with  Preparation  :  (  5  )  Chords  of  the  Diminished  yth  : 
(  6 )  Chords  of  the  Augmented  6th  in  the  three  forms, 
on  the  Dominant  Root,  also  on  the  Supertonic  Root : 
(  7  )  Altered  Chords  :  (  8  )  Attendant  Chords  :  (  9  )  Mod- 

ilation  :    (  10  )    Passing-Notes  :    (  1 1  )    Changing-Notes  : 

(' 12  )  Suspensions:  (13)  Retardations:  (14)  Antici- 
pations: (15)  Sequences:  (16)  Trills  with  various 

sidings:  (17)  Turns:  (  18  )  Mordents:  (i9)Appog- 
giaturas  :  (  20  )  Use  of  the  Old  clefs. 

How  to  Study  the  Above. 

(or.)  First  Step :  Take  one  subject  at  a  time,  and, 
practising  systematically  through  all  the  keys,  form  ex- 
amples in  connection  with  a  suitable  preceding  chord 
(  a  proper  introduction  )  and  a  suitable  chord  to  follow 
^  a  proper  continuation  ) .  Do  not  try  at  this  period  to  pro- 
duce a  complete  musical  thought  (  pupils  frequently  make 


HARMONY  SIMPLIFIED.  223 

the  mistake  of  attempting  so  much  that  the  immediate 
object  is  lost  to  view  ) ,  but  simply  learn  the  use  of  the 
particular  subject  under  consideration. 

(3.)  These  studies  should  be  made  both  at  the  key- 
board and  in  writing. 

(c.)  Analyze  examples  from  standard  writers. 
Examine  all  music  with  which  you  come  in  contact,  look- 
ing for  instances  of  the  points  which  you  desire  to  learn, 
and  noticing  their  treatment. 

(</.)  Persist  in  practising  each  subject  till  its  use 
becomes  thoroughly  familiar. 

(  e.)  2nd  Step :  Compose  complete  phrases  con- 
taining illustrations  of  the  point  under  consideration. 

(f.)  Improvise  short  phrases,  containing  the  de- 
sired points. 

(,£"•)  Jrd  Step :  Take  two  subjects  and  try  to  intro- 
duce them  alternately,  or  as  they  suggest  themselves. 

( h.)  The  pupil  is  warned  against  allowing  too 
much  outside  matter  to  enter  into  these  improvisations, 
for  if  he  wanders  in  search  of  effect  of  any  kind,  he  at 
once  forgets  the  object  of  the  study,  viz.,  to  gain  such 
control  as  will  enable  him  to  introduce  at  will  the  various 
subjects  studied. 

349.  It  will  be  found  that  after  thorough  study  of  this 
branch  of  Harmony,  the  command,  of  the  chords  and  their 
connections,  and  of  the  means  of  giving  variety,  will  be 
greatly  increased.  And  at  the  same  time  the  musical 
thoughts  will  flow  more  freely,  because  the  power  of 
expression  has  been  developed. 

After  composing  phrases  as  above,  the  pupil  will 
naturally  attempt  to  construct  little  pieces,  by  uniting 
several  phrases.  For  this  he  will  need  special  guidance, 
which  is  supplied  in  the  chapter  on  Form.  (  See  §  359, 
et  seq.} 


224  HARMONY  SIMPLIFIED. 

• 

CHAPTER  XVIII. 

ANALYSIS   AND   FORM. 

350.  In  a  work  like  the  present  it  will  be  impossible  to 
give  more  than  a  mere  introduction  and  general  outline 
of  the  subject,  leaving  matters  of  detail  to  books  which 
are   devoted   exclusively  to  this  department   of  musical 
study. 

Analysis  means  taking  apart  or  dissecting,  and  is  the 
opposite  of  Synthesis,  which  means  putting  together  or 
constructing. 

In  considering  the  structure  ot  a  composition,  or  ana- 
lyzing it,  it  is  natural  that  it  should  first  be  divided  into 
its  two  or  three  main  portions,  these  portions  being  after- 
ward taken  up,  one  at  a  time,  and  subdivided  and  exam- 
ined till  all  the  details  of  construction  are  clear. 

Each  of  the  different  Movements  of  a  composition 
(for  example,  a  Sonata),  is  considered  as  a  complete 
structure ;  but  all  are  related  to  each  other  by  the  succes- 
sion of  keys  and  by  the  relationship  of  the  musical  thoughts 
ai  each.  The  work  of  the  Analyst  is,  then,  to  take  a  com- 
plete movement  and  show  its  component  parts  and  details 
of  construction. 

351.  The  basis  of  consideration  in  tracing  the  larger 
divisions  of  a  movement  is,  primarily,  the  Theme  and  the 
different  ways  of  repeating  it.     The  first  thing  is,  then, 
to  understand  something  of  the  Theme. 

The  Theme,  or  Subject,  is  like  the  text  of  a  sermon ; 
we  do  not  expect  to  hear  it  (the  text)  constantly  repeated, 
but  it  is  given  out  or  announced  at  the  beginning;  is 
often  explained,  bit  by  bit;  is  considered  from  different 
points  of  view ;  and  at  the  close  there  is  a  sort  of  recapit- 


SIMPLIFIED.  22$ 

ulation  or  review.  So  with  the  Theme.  After  it  is 
announced  other  matter  is  introduced,  enlarging  upon  it 
as  it  were.  Next,  it  may  appear  in  little  pieces,  called 
Motives,  which  are  worked  out,  giving  unity  as  well  as 
variety.  Of  course,  a  number  of  keys  are  introduced,  but 
they  are  usually  related  to  one  another  very  closely.  How 
to  find  the  Theme  will  be  shown  in  §  354,  where  further 
particulars  and  an  illustration  will  be  found. 

Form. 

352.  Form  relates  to  the  manner  or  order  of  introduc- 
ing the  various  keys,  the  number  of  subjects,  the  manner 
of  their  repetition,  etc., —  in  other  words,  the  design  in 
constructing.  There  are  various  forms,  such  as  the  So- 
nata-Form, the  Rondo-Form,  the  Dance-Form,  the  Pri- 
mary Form,  or  Song-Form,  etc.  These  forms  vary  in 
their  design  as  above  mentioned. 

The  Sonata-Form. 

The  Sonata-Form  being  a  standard,  and  affording 
proper  material  for  analysis,  will  be  considered  first. 
The  Sonata-Form  does  not  relate  to  the  Sonata  as  a  whole, 
but  merely  to  the  fii'st  movement.  The  other  movements 
are  usually  written  in  the  Rondo-,  Song-,  or  Primary 
Form.  The  first  movement  of  a  Sonata  will  therefore  be 
considered. 

Two  Subjects : — In  the  Sonata-Form  two  subjects,  or 
themes,  are  found.  One  is  in  the  key  of  the  Tonic  (the 
original  key  of  the  piece  ) ,  and  the  other  in  the  key  of 
the  Dominant. 

Three  Divisions : —  There  are  usually  three  divisions 
in  the  movement.  They  are  distinguished  by  the  group- 
ing of  the  keys  and  themes.  The  treatment  of  the  two 
themes,  the  order  of  the  keys,  and  the  three  divisions,  are 
shown  in  the  subjoined  synopsis. 


226 


HARMONY  SIMPLIFIED. 


353-  Synopsis  of  Sonata-Form. 

1.     Key  of  Tonic  :  ist  Theme. 
11.     Connecting-Passage,  mod- 
ulating to 


III.  2nd  Theme,  in  ke}'  of  Dom- 

inant. 

IV.  Supplementary  matter  and 

Codetta.  ; 

V.     Development,  or  Free  Fan- 
tasia,   using   short   motives 
from  either  theme,  and  pass- 
ing  through    various    keys 
without    much    restriction, 
leading  back    to    key     of 
Tonic. 
VI.     Repetition  of  ist  Theme  in 

original  key. 
VII.     Connecting-Passage,     not 

modulating. 
VIII.     2nd  Theme,  not  in  the  Dom- 


First  Part.  Is  u- 


j.  sually  followed 
by  double  bar. 


Second  Part. 
.  Not  followed 
by  a    double 
bar. 


•  Third  Part. 


inant  key,  as  before,  but 
in  the  Tonic. 

IX.     Supplementary  matter. 
X.     Closing  Passage,  or  Coda. 
N.  B.     There  are  many  modifications  of  the  above, 
which  cannot  be  described  in  this  sketch,  but  the  pupil 
should  attempt  to  note  and  describe  them. 

Application. 

354.  The  pupil  should  now  take  some  examples,  and 
try  to  locate  the  various  points  mentioned  above.  It  will 
be  easy  to  find  the  Development  if  the  double  bar  is 
present,  likewise  the  modulatory  passage  and  the  key  of 
the  Dominant ;  also  where  the  third  part  begins  with  the 


HARMONY  SIMPLIFIED.  227 

return  to  the  key  of  the  Tonic.  (  The  pupil  may  now 
trv  to  find  these  points  in  various  examples.) 

How  to  find  the  Theme: — In  Sonatas  of  simple  con- 
struction, the  Theme  usually  begins  with  the  first  mea- 
sure of  the  composition,  unless  a  short  introduction  is  given, 
which  introduction  is  easily  discovered  by  its  character. 
It  is  more  difficult  to  find  the  exact  close  of  the  Theme 
without  special  investigation,  as  shown  below. 

The  Theme  should  be  more  or  less  complete  in 
itself.  This  does  not  imply  that  a  full  close  should  mark 
the  end :  on  the  contrary,  the  last  note  of  the  theme  can 
be,  and  often  is,  the  first  note  of  a  supplementary  section 
or  of  the  modulating  passage. 

(a.)  If  the  original  key  is  not  soon  restored  after  a 
modulation,  but  goes  on  into  the  key  proper  for  the  2nd 
theme,  we  may  know  that  the  ist  theme  has  ceased,  and 
that  the  modulatory  passage  has  begun.* 

(  6.)  There  is  no  definite  standard  for  the  length  of 
the  Theme.  It  may  be  of  four  measures,  and  it  may  be 
of  fiftv ;  it  may  have  repetitions  and  modulations  (  short 
ones  only)  ;  or  half-closes  and  other  irregular  features, 
which  are  at  first  confusing.  Therefore,  the  best  way 
to  get  the  first  impression  is  to  watch  the  modulations, 
and  note  whether  they  return  to  the  tonic  key  or  lead  on 
to  the  key  of  the  2nd  theme. 

(  c.)  Compare  that  which  is  thought  to  be  the 
theme  with  the  recapitulation,  i.  e.,  VI  of  the  synopsis. 
If  the  two  coincide,  the  pupil  may  be  sure  that  he  has 
found  the  theme.  NOTE.  By  comparison  of  the  theme 


•  A  change  of  key  often  occurs  without  any  indication  in  the  signature. 
Therefore,  the  pupil  must  carefully  observe  the  chords  themselves,  watching 
the  accidentals  and  all  Chords  of  the  Seventh. 

In  studying  the  chords,  be  careful  tc  exclude  all  Passing  and  Auxiliary 
Dotes  from  consideration. 


228  HARMONY  SIMPLIFIED. 

with  its  repetition,  the  exact  ending  of  the  theme  may  oa 
found  ;  for  only  so  much  as  is  a  part  of  the  theme  prooet 
is  repeated  in  the  recapitulation.  Where  the  repetition 
digresses  from  the  exact  notation  of  the  first  presentation, 
usually  marks  approximately  the  end  of  the  theme  proper. 
(There  may  be  exceptions  to  this  rule,  as  there  are  to 
most  rules,  but  it  will  prove  a  valuable  guide  in  tnt 
majority  of  cases.) 

To  trace  the  2nd  Theme:  —  It  usually  begins  soon 
after  the  modulation  to  the  Dominant  key  is  established. 
But,  to  be  sure  of  its  exact  beginning  and  ending,  com- 
pare with  the  recapitulation.  That  which  was  in  the  key 
of  the  Dominant  should  be,  at  the  repetition,  in  the  key 
of-  the  Tonic. 

When  the  pupil  can  distinguish  the  boundaries  of  the 
first  and  second  subjects,  the  development,  the  modula- 
tory  passages  connecting  the  different  parts,  and  the  re- 
patitions  of  the  themes,  as  outlined  above,  it  will  not  be 
difficult  to  recognize  the  supplementary  matter  and  clos- 
ing passages  or  coda,  for  they  would  be  contained  in  the 
matter  not  already  classified. 

As  mentioned  before,  there  will  be  many  modifica- 
tions of  these  features,  some  of  them  occasionally  being 
omitted  entirely,  and  the  order  of  keys  and  the  arrange- 
ment of  the  matter  being  sometimes  very  different  from 
the  order  here  indicated.  But  in  this  chapter  it  is  possi- 
ble to  treat  only  of  the  standard  form,  leaving  all  excep- 
tions to  works  devoted  entirely  to  this  subject. 

355.  It  will  be  well  to  begin  by  analyzing  a  Sonatina 
(a  Kttle  sonata),  as  the  construction  is  more  simple  and 
the  various  parts  more  definitely  indicated  than  in  the 
Sonata. 

Owing  to  the  limited  space  between  the  staves,  it  is 


SIMPLIFIED. 


229 


necessary  to  use  abbreviations  to  mark  the  themes,  con- 
necting-passages, etc.  The  following  are  suggested  and 
used  in  referring  to  the  different  parts  : — 

i st  Theme,  I.  T. ;  Connecting- Passage,  C.  P.;  2nd 
Theme,  II.  T. ;  Supplementary  Matter,  S.  M. ;  Coda,  C. ; 
Development,  D. ;  Half-Close,  %  Cl. ;  etc. 

Before  beginning  the  analysis,  the  measures  should 
be  numbered  for  reference.  The  beginning  of  the  ist 
and  2nd  themes  should  be  marked  first,  leaving  the  close 
of  the  themes  to  be  decided  when  the  C.  P.,  S.  M.,  and  C. 
are  found. 

Exercises. 

Taking  in  turn  the  sonatinas  indicated  below,  the 
pupil  will  find  and  mark  the  various  points  outlined  in 
the  synopsis,  in  the  following  order :  —  I :  III :  V :  II : 
IV:  VI:  VII:  IX:  X.  (See  synopsis,  §  353.) 

Or   I:  VI:      HI:  VIII:     Il7  VII :     V:     IX:    X, 

tracing  them  in  pairs  as  indicated  by  the  brackets.  For 
example,  taking  the  Sonatina,  Op.  49,  No.  2,  by  Beet- 
hoven. 

f        I  begins  at  measure  i  (  ends  at  meas.  8) . 
1    VI  begins  at  measure  67  (ends  at  meas.  74). 
(    III  begins  at  measure  20  (  ends  at  meas.  36) . 
1  VIII  begins  at  measure  87  (  ends  at  meas.  105). 
(       II  begins  at  measure  8. 
1   VII  begins  at  measure  74. 
V  begins  at  measure  53. 
IX  begins  at  measure  105. 
X  begins  at  measure  116. 
The  sonatinas  to  be  analyzed  are  : — 
Clementi.,  Op.  36,  No  i.       (N.  B.    The    C.    P.    is 

short ;  modulation  effect- 
ed by  a  Half-Close.) 


230  HARMONY  SIMPLIFIED. 

Clementi,  Op.  36,  No  2. 


Clementi,  Op.  36,  No  3. 
Clementi,  Op.  36,  No  4. 
dementi,  Op.  36,  No  5. 
dementi,  Op,  36,  No  6. 
Kuhlau,  Op.  20,  No.  i. 
Kuhlau,  Op.  20,  No.  2. 


Kuhlau,  Op.  20,  No.  3. 
Kuhlau,  Op.  55,  No.  i. 

Kuhlau,  Op.  55,  No.  2. 

Haydn,  Sonatina  in  C. 
Mozart,  Sonata  in  C. 


(  C.  P.  omitted.) 

(Development  is  a  free  ren- 
dering of  I.  T.,  which  is 
therefore  not  given  again 
in  the  Recapitulation.) 

(Short  C.   P.,  one  mea- 
sure only.) 
(  C.  P.  omitted  ;  mod.  by 


( Irregular  repetition  of 
I.  T.  in  the  Sub-Dom. 
instead  of  Tonic.) 

Beethoven,  Sonata  Op.  49,  No.  i.      (See   ist  Note, 

below.  In  the  Reca- 
pitulation the  I.  T.  is  in 
left  hand.) 

NOTE.  If  a  Sonata  is  written  (  i.  e.,  begins  )  in  a  minor  key,  the 
second  subject  is  usually  in  the  parallel  major  key  rather  than  in  the 
Dominant. 

NOTE.  All  the  above-mentioned  Sonatas  and  Sonatinas  may 
be  found  in  the  "  Sonatina  Album, "  Vol.  51  of  Schirmer's  Library,  in 
an  inexpensive  and  compact  form. 

Harmonic  Analysis. 

356.  The  analysis  of  the  Form  has  been  shown  above. 
As  soon  as  the  form  is  outlined  in  any  of  the  above  exam- 
ples, the  pupil  should  turn  his  attention  to  the  harmonic 
construction.  Each  chord  should  be  marked  according 


HARMOATY  SIMPLIFIED. 


231 


to  the  degree  of  the  scale  upon  which  it  is  founded  (  sim- 
ply mark  them  as  required  in  previous  chapters  )  ;  the 
chords  should  be  figured,  attendant  chords  indicated, 
modulating  chords  marked  by  the  letter  showing  the  new 
key,  and  all  Passing  and  Auxiliary  notes  distinguished 
from  the  essential  notes  of  the  chord. 

Rondo-Form. 

357.  In  §  352  it  was  stated  that  Form  relates  to  the 
manner  of  introducing  different  keys,  and  of  treating  the 
subjects,  repetitions,  etc.     In  the  Rondo-Form  we  may 
expect  to  find  a  different  design  from  that  shown  in  the 
Sonata-Form. 

A  chief  characteristic  of  the  Rondo-Form  is  the  fre- 
quent recurrence  of  the  Subject  or  principal  theme. 
Another  characteristic  is  the  freedom  of  the  order  in 
which  the  different  keys  succeed  each  other.  In  the  sim- 
plest form  (  there  are  several  varieties  of  the  Rondo ) 
there  is  but  one  subject,  which  is  repeated  several  times, 
an  interlude  occurring  after  each  presentation  of  the  theme. 
Variety  is  imparted,  (  i  )  by  allowing  the  interludes  to 
digress  into  various  keys  (  often  a  different  key  for  each 
interlude ),  and  (  2  )  by  the  varying  treatment  of  the 
theme  in  the  repetitions. 

In  the  more  elaborate  forms  of  the  Rondo  there  are 
two,  three,  or  more  themes,  and  the  requisite  interludes 
(also  called  episodes). 

For  examples  of  the  Rondo,  see  the  movements 
marked  "Rondo"  in  the  list  mentioned  in  §  355. 

Also  Beethoven,  Sonata  Op.  2,  A  maj.,  Largo. 

Beethoven,  Symphony  No.  5,  Andante. 

Beethoven,  Sonata,  Op.  10,  No.  3,  Rondo. 

Exercises. 

358.  Taking  the  examples  mentioned  above,  indicate 


23  2  HARMONY  SIMPLIFIED. 

the  principal  subjects,  mark  the  keys  in  which  the  epi 
sodes  are  written,  and  try  and  discover  if  there  is  a  second 
(  also  third  )  subject.     Also  mark  the  chords. 

The  Primary  Form. 

This  form,  though  simpler  than  either  of  those  already 
shown,  cannot  well  be  explained  without  a  digression,  as 
follows : — 

Definitions. 

359.  A  Phrase : —  is  a  more  or  less  complete  musical 
thought.  Its  distinguishing  characteristic  is  the  presence 
of  a  cadence  to  complete  it.  The  cadence  need  not  be  a 
perlect  one,  a  cadence  of  any  sort  being  sufficient. 

Phrases  are  usually  of  two,*  four,  or  eight  measures, 
though  they  may  be  of  three,  five,  six,  seven,  or  other 
odd  number  of  measures. 

A  Period:  —  is  the  next  larger  division,  and  is 
formed  from  two  Phrases,  each  phrase  of  course  having 
its  own  cadence.  It  is  required  that  the  two  phrases 
shall  bear  a  certain  relation  to  each  other,  the  second  ap- 
pearing as  a  sequel  to  the  first,  responding  to  or  complet- 
ing it.  When  the  two  phrases  stand  in  this  relation  to 
each  other,  the  first  is  called  the  Thesis  (  Proposition, 
or  Question) ,  and  the  second  phrase  is  called  the  Antith- 
esis (  Conclusion,  or  Answer  ).  The  first  phrase  should 
suggest  or  lead  toward  the  second ;  therefore,  it  should 
not  be  complete  in  itself  either  with  regard  to  the  melody 
or  harmony — (  should  not  end  with  a  perfect  cadence). 
The  second  phrase,  which  completes  the  Period,  may  end 
with  a  more  pronounced  Close.  As  phrases  vary  in  the 


*  A  Phrase  of  two  measures  is  technically  called  a  Section.  Four-measure 
phrases  are  usually  chosen  to  form  the  Thesis  or  Antithesis  of  a  Period,  tl  ough 
there  may  be  two  Sections  in  such  a  Thesis  or  Antithesis. 


HARMONY  SIMPLIFIED. 


233 


number  of  measures,  the  Periods,  being  formed  by  the 
union  of  two  phrases,  will  vary  also. 

A  Motive: —  is  a  germ  of  thought,  which  is  capable 
of  elaboration.  It  usually  consists  of  but  a  very  few 
notes,  which  have  a  distinct  rhythmic  or  melodic  effect. 
These  fragments  of  thought  are  repeated  in  different  ways 
and  elaborated  until  they  constitute  a  large  part  of  the 
material.  Some  compositions  are  largely  developed  from 
motives,  others  from  more  independent  melodies. 

To  illustrate  the  above  definitions,  turn  to  Kuhlau, 
Sonatina  Op.  20,  No.  i. 

The  Phrase  is  shown  in  the  first  four  measures  (also 
in  each  succeeding  division  of  four  measures  ). 

The  Period  is  shown  in  the  first  eight  measures 
(  also  in  the  second  eight  )  . 

The  Motive  is  shown  in  the  first  three  notes  ( a 
rhythmic  motive,  consisting  of  a  dotted  sixteenth-note 
followed  by  a  thirty-second  )  . 

The  Primary  Form.    Also  called  Liedform,  or 
Song-Form. 

360.  When  two  eight- measure  Periods  a.e  used  in 
conjunction,  they  form,  under  a  certain  condition,  a  small 
Two-part  Primary  Form.  The  condition  is,  that  the  periods 
shall  stand  in  the  mutual  relation  of  Thesis  and  Antithe- 
sis, or  Question  and  Answer.  Thus  we  have  the  principle 
of  Thesis  and  Antithesis  illustrated  not  only  in  the  con- 
struction of  each  Period,  but  also  in  the  relation  of  the 
Periods  to  each  other.  To  comply  with  this  condition,  it 
is  necessary  to  have  the  Antithesis  of  the  second  Period 
similar  to  the  Antithesis  of  the  first  Period,  though  the 
Thesis  of  the  second  period  may  differ  from  the  Thesis  of 
the  first  period.  For  example,  see  Kuhlau,  Op.  55,  No. 
2,  Cantabile.  Here  the  Antithesis  of  the  second  Period 


234  HARMONY  SIMPLIFIED. 

cannot  be  exactly  like  that  of  the  first  Period,  since  the 
first  closes  in  the  Dominant,  while  the  movement  (of 
which  the  second  Antithesis  is  the  close)  must  end  in 
the  key  in  which  it  began. 

Many  Folk-Songs,  Hymn-tunes,  and  simple  songs 
are  written  in  this  form. 

361.  Where  the  two  Periods  do  not  stand  in  the 
Relation  of  Thesis  and  Antithesis,  they  do  not  form  the 
Primary  Form,  but  simply  a  Double  Period,  or  Period- 
Form.  There  are  various  forms  of  cadences  found  in 
the  phrases  of  the  Primary  Form,  but  a  discussion  of 
them  would  extend  beyond  the  limits  of  this  volume. 
In  addition  to  the  Two-Part  Primary  Form  just  described, 
there  are  the  Three-Part  Primary  Form,  produced  by  inter- 
polating a  new  part  between  the  two  periods  of  the 
Two-Part  Form  (for  example,  see  Beethoven,  Op.  49, 
No.  2,  Tempo  di  Minuetto.  The  new  part  extends 
from  the  8th  to  the  1 2th  measure)  ;  and  the  Large  Primary 
Form,  produced  by  employing  phrases  of  eight  measures, 
producing  sixteen-measure  Periods.  Phrases  may  also 
be  extended,  abbreviated,  or  may  overlap. 

Exercises. 

Refer  to  the  examples  given  in  §  355,  and  try  to 
analyze  the  themes,  marking  the  phrases,  periods,  and 
motives ;  trying  to  discover  the  relation  of  Thesis  and 
Antithesis  in  the  phrases  and  Periods,  thus  forming 
Period  and  Primary  Forms  where  possible. 

Comparison  of  the  Preceding. 

With  reference  to  the  preceding,  it  should  be  noticed 

that  the  Theme  is  the  means  by  which  the  Sonata  and  the 

Rondo-Forms  are  judged ;  while  the  Phrase  is  the  basis 

(or   analyzing  the  Period-form  and  the  Primary   form. 


HARMON*  SIMPLIFIED.  335 

Of  course,  the  Theme  of  the  Sonata  and  Rondo  may  be 
analyzed  to  show  their  construction, —  whether  in  the 
Period  or  Primary  Form,  if  either.  The  Period  and  the 
Primary  Forms  may  be  said  to  represent  the  different 
methoas  of  construction  or  of  putting  the  phrases  together, 
i.  e.,  the  details  of  the  composition  ;  while  the  Sonata  and 
the  Rondo  are  concerned  with  the  arrangement  of  the 
larger  portions  thus  produced. 

A  succession  of  Phrases  without  relation  to  each 
other  produces  a  Fantasia.  When  the  Phrases  are  related 
to  each  other  as  Thesis  and  Antithesis,  a  Period  is  pro- 
duced :  when  the  successive  Periods  are  not  related  to  each 
other  (  Thesis  and  Antithesis  ),  they  produce  Period-Form. 
When  the  Periods  are  related  to  each  other  (  Thesis  and 
Antithesis),  they  produce  Primary  Form. 

In  addition  to  the  examples  mentioned  in  §  355,  the 
pupil  should  analyze  a  number  of  Piano-Studies  or  Etudes, 
which  are  usually  written  in  the  Liedform. 

It  will  also  be  well  to  analyze  the  Sonatas  of  Mozart 
and  Haydn  before  attempting  those  of  Beethoven,  which 
are  more  complex  and  obscure. 

The  pupil  may  now  be  encouraged  to  compose  Hymn- 
tunes,  Songs  Without  Words,  and  other  little  pieces,  taking 
some  standard  work  as  his  model  as  to  length  of  themes, 
variety  of  keys,  etc.  Further  instruction  in  regard  to 
Form  may  be  found  in  "  Musical  Form,"  Bussler-Cornell, 
N.  Y. :  G.  Schirmer. 

If  the  pupil,  through  his  studies  in  Harmony,  has 
become  able,  and  through  this  little  introduction  to  Mus- 
ical Analysis  has  become  sufficiently  interested  in  the  con- 
struction of  Music,  to  continue  his  investigations  in  the 
realm  of  Art,  the  purpose  of  this  elementary  work 
have  been  attained. 


ALPHABETICAL  INDEX. 


THE    FIGURES    REFER    TO    THE    PARAGRAPHS 

Alteration,  chromatic,  44,  246. 

"  harmonic,  246. 

"  melodic,  246. 

Altered  chords,  238  et  seq.;  255  et  seq. 
Alto,  114. 

Ambiguous  chords,  254. 
Analysis,  350  et  seq. 

"        harmonic,  356. 
Anticipation,  309-311. 
Antithesis,  359. 
Appoggiatura,  320. 
Attendant  chord,  269  et  seq.;  278. 

"  "        for  each  major  and  minor  triad,  270. 

"  "        in  modulation,  278  et  seq. 

"  "        resolution  of,  266-269. 

Augmented  interval,  58. 

"  "  resolution  of,  154. 

"        Sixth,  chord  of,  222. 

"        Six-Three,  chord  of,  225. 

*        Six-Four-Three,  chord  of,  226. 

"        Six-Five-Three,  chord  of,  227. 

"        Sixth-chord  derived  from  Supertonic,  229. 

"        Triad,  93. 
Authentic  Cadence,  190. 
Auxiliary  note,  320  et  seq. 

Bass,  compass  of,  114. 
Broken  chords,  1 18. 

Cadences,  Deceptive,  False,  Half-Close,  190. 

"        Imperfect,  Modulatory,  190. 

"        Perfect,  Plagal,  Authentic,  190. 
Cadencing  Resolution,  1 58. 
Cantus  Firmus,  341. 
Change  of  Root,  243. 

"     of  Mode,  299 
(236) 


/NJJEX. 

Changing-nott,  320. 
Chant,  Double,  343. 
Chords,  Altered,  238  et  seq.;  255  et  sey. 

"      Ambiguous,  254. 

"      Attendant,  269  et  seq,;  278. 

"      Broken,  118. 

"      Dependent,  150-155,  157 

"      Foreign,  265  et  seq, 

44      Fundamental,  90,  239,  247-255. 

"      Independent,  150-155. 

"      Interpolated,  254. 

"      Inversions  of,  125,  172. 

"      Passing,  318. 
Chord  of  Augmented  Sixth,  222  et  seq* 

"    "  Diminished  Seventh,  210  et  seq. 

"    "  Dominant  Seventh,  156  et  seq. 

"    "  Eleventh  and  Thirteenth,  337, 

"    "  Fourth  and  Sixth,  129,  330. 

"    "  Nature's,  90. 

44    "  Seventh  and  Ninth,  204.^- 

"    "  Seventh  on  7th  degree,  179. 

"   "      «          Principal,  176. 

succession  of,  185. 

"    "      "          Secondary,  176. 

''    "  Sixth,  129;  Neapolitan  Sixth,  259  et  seq. 
Chromatic  Alteration,  44,  246. 

"         Half-Step,  44. 

44         Interval,  78. 

44         Scale,  43. 
Circle  of  Fifths,  22-24. 

"  of  Keys,  13-23,  42. 
Clefs,  C,  336. 
Close,  Half,  190. 
Close  Position,  101. 
Closing  Formula,  191,  295. 
Collateral  Triads  ;  See  Secondary. 

"         Seventh-Chords,  176. 
Common  Note,  102. 

Complementary  Intervals,  Addendum,  under  by 
Connection  of  Triads,  97,  101-110,  119. 

"          of  Keys,  285  et  seq. 
Consecutive  Fifths,  98. 
**  Octaves,  98. 


2j8  INDEX. 

Consonances,  Perfect  and  Imperfect.  75,  326,  327. 
Consonant  Intervals,  75. 
Continuity,  Tendency  of,  153. 
Contrary  Motion,  100. 
Cross  Relation,  328. 

Deceptive  Cadence,  190. 
Degrees  of  Scale,  2. 
Dependent  Chords,  150-155,  157. 
Diatonic,  3  {foot-note ). 

"         Half-Step,  44. 

"        Interval,  78. 

11        Scale,  3 
Diminished  Interval,  58. 

"  "  Resolution  of,  154. 

"  Seventh,  chord  of,  210  et  seq. 

"  Triad,  93. 

Discovery  of  Roots  of  Triads,  126 ;  of  chords  of  tne  7th,  172. 

",         of  Roots  of  Fundamental  dependent  chords,  249-253. 

"         of  Keys,  18  (foot-note'),  252. 
Dispersed  Harmony,  338. 

Dissonances,  Essential  and  Unessential,  325;  Preparation  of,  181. 
Dissonant  Intervals,  75. 
Distribution  of  Parts.  164. 
Dominant,  34. 

"  Seventh,  chord  of,  i$6et seq. 

"  Harmony,  various  forms  of,  228. 

Double  Sharps,  7. 

"     Flats,  9. 
Doubling;  95. 

"          of  Third,  162. 

"         of  Dissonant  or  Tendency-Hptes,  102, 183. 

Eleventh,  Chord  of,  337. 
Enharmonic,  78. 
Essential  Notes,  325. 

"        Dissonances,  325. 
Extended  Intervals,  69. 

False  Cadence,  190. 
Fifths,  Circle  of,  22-24. 

"    Consecutive,  98-100. 

*    Hidden,  134. 


INDEX.  239 

Fifths,  Omission  of,  158. 

Figured  Bass,  in,  122,  123,  127-132. 

Five- Part  Harmony,  339. 

Foreign  Chords,  265  et  seq. 

Form,  352  et  seq. 

Formula,  Closing,  191. 

"        for  Modulation,  200. 

"        for  comparing  chords  by  their  intervals,  239,  248. 
Four-Part  Writing,  97. 
Four-lwo,  chord  of,  172. 
Free  Suspensions,  320. 
French  Sixth,  228. 
Fundameutal  Chords,  90,  239,  247-255. 

German  Sixth,  228. 
Great  Staff,  336. 

Half-Close,  190 
"     Step,  I. 

"        "      Chromatic,  Diatonic,  44. 
Harmonic  Alteration,  246. 

"          Analysis,  356. 

"         Minor  Scale,  35. 

"          Tendencies,  154,  157. 
Harmonics,  Natural,  90. 
Harmonizing  Melodies,  340  et  seq. 
Hidden  Fifths  and  Octaves,  134,  163. 
Historical,  45  et  seq  ;  80,  and  202. 

Imperfect  Cadence,  190. 

"         Consonance,  75. 
Independent  Chords,  150-155. 
Influences,  161,  192. 
Inner  Parts,  97. 
Interpolated  Chords,  2C4. 
Interval,  53  et  seq. 
Intervals,  Augmented,  58. 

"         Complementary,  Addendum,  under  89. 

"         Chromatic,  78. 

"         Consonant,  75. 

"         Diatonic,  78. 

"         Diminished,  58. 

"         Dissonant,  75. 

"         Inversion  of,  70. 

«        Major,  58. 


240  INDEX. 

Intervals,  Measurement  of,  59-68. 

«         Minor,  58. 

"         Normal,  58. 

Perfect,  58,  73,  76. 
Table  of,  64,  71,72. 
Inversion  of  Chords  of  the  7th,  172  et  seq. 

"        of  Intervals,  70. 

"         Triads,  125,  et  seq. 
Inverted  Pedal,  323. 
Italian  Sixth,  228. 

Key-note,  10. 
Keys,  ii. 

"     Connection  of,  285  et  seq. 

«     Related,  32,  334. 

Leading-Hote,  34,  46,  152,  250,  252;  Doubling  of,  162. 
Licenses,  331. 

Major  Interval,  58. 

"      Scale,  i ;  Triad,  93. 
Marking  Chords,  92,  93. 
Measurement  of  Intervals,  59  et  seq. 
Mediant,  34. 

Melodic  Alteration,  246;  Minor  Scale,  35;  Tendencies,  152,  157. 
Minor,  Interval,  58 ;  Relative,  39 ;  Mode,  36 ;  Scale,  35 ;  Triad,  93. 
Mode,  36 ;  Change  of,  299. 
Modulation,  276  et  seq. 
Modulatory  False  Cadence,  190,  195. 
Motion,  Contrary,  Oblique,  Parallel,  100. 
Motive,  359. 

Naming  the  Octaves,  335. 
Natural  Resolution,  155,  173,  266. 
Nature's  Chord,  90. 
Neapolitan  Sixth,  259  et  seq. 
Neighboring  Tone,  321. 
Ninth,  Chord  of,  204 ;  Interval  of,  69. 
Normal  Interval,  58,  59. 
Non-cadencing  Resolution,  192-198. 

Oblique  Morion,  100. 

Octaves,  Consecutive,  98 ;  Hidden,  134,  163;  Naming  of,  335. 

Omission  of  the  Fifth,  158. 


IfifDEX.  241 

Open  Position,  101. 

Opposition  of  Tendencies,  165-167. 

Order  of  Sharps,  16. 

Organ-point,  322. 

Outer  Parts,  97. 

Parallel  Motion,  100. 

Part-leading,  Principles  of,  161-169. 

Parts,  Distribution  of,  164;  Outer,  Inner.  97. 

Part-writing,  97,  in. 

Passing-Chords,  318;  Notes,  315. 

/Wa/-Point,  322  ;  Inverted,  323. 

Perceptive  Faculties,  47  et  seq.;  81  et  seq. ;  137  and  203. 

Perfect  Cadence,  190  ;  Consonance,  75;  Fifth,  58;  Interval,  58. 

Period,  359 ;  Period-Form,  361. 

Phrase,  359. 

Plagal  Cadence,  190. 

Position,  96 ;  Open,  Close,  101. 

Preparation  of  Dissonant  Intervals,  181 ;  of  Seventh,  181 ;  of  Suspen 

sions,  302. 
Primary  Form,  360. 
Prime,  56. 

Principal  Chord  of  the  7th,  176 ;  Triads,  94. 
Principles  of  Chord-Construction   or   Building,     91  ;  of  Attendant 

Chords,  266-275;  °f  Resolutions,  156-159;  of  Part-Leading,  161- 

169;  of  Tendencies,  152-155. 
Prominence  of  Outer  Parts,  163. 

Related  Keys,  32,  334. 

Relation,  Cross,  328  ;  of  Dominant  to  Tonic,  266. 

Relative  Sharpness,  29,  250 ;  Minor,  39. 

Resolution,  Cadencing,  158;  Non-cadencing,  192-198;  Natural,  of 
Chord  of  the  7th,  173;  of  Augmented  Sixth-Chords,  225-228;  of 
Dissonances,  150,  155,  157  ;  of  Suspensions,  302. 

Retardations,  312. 

Rondo-Yorm,  357. 

Roots,  Discovery  of,  126,  249,  253 ;  Change  of,  243. 

Scale,  i-io ;  Chromatic,  43 ;  Diatonic,  3  ;  Major,  i  et  seq. ;  Melodic  Mi- 
nor, Harmonic  Minor,  35. 

Secondary  Chords  of  the  7th,  176,  187  ;  Triads,  94. 
Sequence,  332,  333. 
Seventh,  Chords  of :  See  Chords. 


3<J2  INDEX. 

Shake,  321. 

Sharps,  order  of,  16. 

Signature,  12,  41. 

Similar  Resolution  of  all  Dependent  Chords,  236. 

Similarity  of  Sound  of  Chords  of  the  Diminished  7th,  215. 

Six-Fin*.  Chord  of,  172. 

Six- Four,  Chord  of,  129,  330. 

Sixth,  chords  of:   See  Chords  ;  Augmented,  chords  of:  See  Chords. 

Sonata-Form,  352  et  seq. 

Soprano,  114. 

Specific  Names,  of  Scale-Notes,  34 ;  of  Intervals,  58 ;  of  Triads,  93. 

S«^-Dominant,  -Tonic,  -Mediant,  34. 

Succession  of  Chords  of  the  7th,  185. 

Supertonic,  34. 

Suspensions,  302;  Free,  320. 

Sustained  Notes,  323. 

Syncopation,  314. 

Table  of  Intervals,  64,  71,  72. 

Tendencies,  Harmonic,  154,  157  ;  Melodic,  152,  157,  201  ;  of  Continu- 
ity, 153;  Opposition  of,  165-167;  to  Remove,  284. 

Tcndency-Noies,  152;  not  to  be  doubled,  162 

Tenor,  114. 

Tetrachord,  45. 

Theme,  351,  354. 

Thesis,  359. 

Third,  doubling  of,  162. 

Third   and  Fourth,  chord  of,  172. 

Thirteenth,  chord  of,  337. 

Tonality,  45. 

Tonic,  34. 

Transposition,  105,  146. 

Triads,  91  ;  Major,  Minor,  Diminished,  Augmented.  93 ;  Principal  and 
Secondary,  94;  Connection  of,  97,  102,  106,  109;  Inversion  of,  125 
et  seq. 

Trill,  321. 

Tritone,  329. 

Turn,  321. 

Unessential  Notes,  325 ;  Dissonances,   325. 

Variety  of  Structure,  301  ft  seq. 
Voices,  Compass  of,  1 14 :  See  Parts. 

Whole  Step,  I. 


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NEW  YORK  BOSTON 

A610 


University  of  California 

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ftc  ""-  LAngeles,  CA  90024-1388 


A     000  058  842     6 


